An introduction to Digital Signal Processing
Felix Donkers
© Felix Donkers
Outline
• Introduction ◦ Definition Digital Signal Processing ◦ Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Title of Presentation Outline
• Introduction ◦ Definition Digital Signal Processing ◦ Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Digital Signal Processing – definition
(Digital) Signal Processing [source: WikipediA ]
DSP is the analysis, interpretation , and manipulation of signals (in the digital domain) .
Signals of interest include sound, images, radar, biological signals such as ECG , and many others .
Processing of such signals includes storage, reconstruction , transmission, separation of information from noise , compression, feature extraction, etc .
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Title of Presentation Digital Signal Processing – definition
Signal improvement Signal feature extraction - beats per minute DSP (music) DSP - color (ambilight)
Signal acquisition Signal synthesis
ACQ SYN
Signal compression Signal transmission
ENC DEC TR REC
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Digital Signal Processing – application fields
Sensor signal processing is still hot & high tech
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Title of Presentation Digital Signal Processing – another example
Mic electronics: • Amplifier • Pre-filtering (conditioning) •Noise filter •Anti-aliasing
ADC DSP DAC
PA electronics: • Post filtering • Smooting filter • Rendering • Power amplifier • Loud speakers
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Digital Signal Processing – application examples
Etc, etc, etc
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Title of Presentation Outline
• Introduction ◦ Definition Digital Signal Processing Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Analoge versus digital signals
• Signals: – Representation of time variant physical measures – E.g. temperature, humidity, speed, weight, light intensity, sound, ..., … A
Analogue signal • Analogue signals: Digital signal – Continuous (often electrical) representation of physical signals. – Amplitude and time continuous
• Digital signals: t – Discrete representations (numbers) of physical signals – Amplitude discrete (vertical grid) and time discrete (horizontal grid)
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Title of Presentation Sensors (some examples)
Microphone Temperature Magnetic field Pressure Accelero- Strain gauge LDR sensor (Hall) sensor sensor meter
Biosensor Photocell CCD Ultrasone sensor Interferro- sensor
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When to use DSP?
• In general: • When you run into the boundaries of the performance of your sensors, actuators and/or overall system.
• Example: temperature measurement • If you’re only interested in rough figures (e.g. +/- 10 °C) • Just use the sensor as is • If you’re interested in fair accuracy (e.g. +/- 1 °C ) • Calibrate the sensor (offset / gain) • If you need accurate figures (e.g. +/- 0.1 °C) • Average multiple measurements (which is already a simple form of DSP)
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Title of Presentation Example : DSP in cell phones
• RF demodulation & channel EQ (for optimal ISI) (GSM, EDGE, GPRS, UMTS, WCDMA, HSDPA, DVB-T, DAB, FM, GPS, …) • Clock extraction & bit detection • Error detection & correction • Audio & video coding (speech, mp3, JPG, MPG, … (de-)compression) • Error concealment (i.e. what to do if error correction fails) • Midi-synthesis (e.g. ringtone) • TTS synthesis (e.g. caller-ID) • Auto – DJ (incl. feature extraction) • Image scaling & enhancements • Audio enhancement (e.g. EQ, virtual surround) • GPS decoding • DTMF synthesis • ……
• Typical mobile phone platform : – DSP for RF demodulation (200MHz) – ARM7 / ARM9 / ARM11 for base band processing (400MHz) 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 13
AD / DA conversion
• Resistor network DACs • 8 – 10 bit resolutions • Up to 10 MHz sampling rates
Ruit
U U U U = −R (* MSB + ... + LSB ) uit uit R 2* R 4* R
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Title of Presentation AD / DA conversion
• Resistor network DACs • 8 – 14 bit resolutions • Up to 10 MHz sampling rates • R-2R network is the mostly used DAC architecture for various applications
2R D D D D D V −= ( 0 + 1 + 2 + 3 + 4 +...... ) out R 2 4 8 16 32
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AD / DA conversion
• Successive Approximation ADC • 8 – 14 bit resolutions • Up to 100 kHz sampling rates • Requires S&H to ‘freeze’ input signal • Often used: • in Measurement & Instrumentation environments
• as function block inside microcontrollers step SAR Vin > Action Vdac ? 1 1000 No
2 0000 Reset 3 0100 Yes
4 0100 Keep 5 0110 Yes 6 0110 Keep 7 0111 No 8 0110 Reset
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Title of Presentation AD / DA conversion
• Resistor network ADCs • 6 – 10 bit resolutions • Up to 10 MHz sampling rates • Often used for video capturing
Comparator XOR Binary Output Output Output 1111111 1000000 111
0111111 0100000 110
0011111 0010000 101
0001111 0001000 100
0000111 0000100 011
0000011 0000010 010
0000001 0000001 001
0000000 0000000 000
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AD / DA conversion
• Delta-sigma ADC • 14-20 resolutions • From < 1Hz up to 100 kHz sampling rates • Often used: • in Measurement & Instrumentation environments • Audio conversion
Digital filter
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Title of Presentation Outline
• Introduction ◦ Definition Digital Signal Processing ◦ Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Time domain versus frequency domain
N = ω +ϕ tf )( ∑ An sin(* n *t n ) = n=1
+
= ω +ϕ tf )( A1 sin(* 1 *t 1) + ω +ϕ A2 sin(* 2 *t 2 ) + ω +ϕ A3 sin(* 3 *t 3 ) + ω +ϕ A4 sin(* 4 *t 4 ) + ω +ϕ A5 sin(* 5 *t 5 )
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Title of Presentation Time domain versus frequency domain
• Test signal
• Music
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Discrete Fourier Transform (DFT)
• To transform a Time Domain Signal into the Frequency Domain (and v.v.)
DFT = Discrete Fourier Transform “1” Σ * e− ωtj
Σ * +
e− ωtjN
Σ *
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Title of Presentation Fast Fourier Transform (FFT)
Fast Fourier Transform (FFT):
2 – is a computation efficient implementation of the DFT ( N*log 2(N) instead of N cycles ) – is available in various of-the-shelf math libraries for numerous platforms (PC, DSP, etc) – often assumes a signal length with a power-of-2 (#samples), e.g. 1024
FFT
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Nyquist / Shannon Theory
time domain A Aliasing
t
• According to Nyquist and Shannon, the sampling frequency should be a least twice the highest frequency of the input signal:
◦ fsampling > 2 * finput
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Title of Presentation Nyquist / Shannon Theory
frequency domain
remember basic trigonomet rics : 1 1 cos( α *) cos( β ) = *cos( α − β ) + *cos( α + β ) fin 2 2
f f f fin, mirror in, mirror LPF in, mirror in, mirror
aliasing !! fs > 2* f max
fs, nok fs, ok fs, ok
5 10 15
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Digital Filters (FIR)
x[n-1] x[n-2] x[n-3] x[n-i] x[n-M] x[n] T T T T T
a0 a1 a2 a3 ai aM * * * * * * y[n] + + + + + +
M tap = zY )( = −n zH )( ∑ an * z zX )( n=0 = + −1 + −2 + −3 +K+ −M • FIR filters: zH )( a0 a1 * z a2 * z a3 * z aM * z – Have an Finite Impulse Response – Have many “filter taps”, implying relatively high computational load – Can not become unstable Do #255 – Can have linear phase response (tranversal filters) Mac x0, y0, a x(R0+N0), x0 y(R4+), y0 End Macr x0, y0, a
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Title of Presentation Digital Filters (FIR)
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Digital Filters for image processing (2D-FIR)
X0,0 ……X0,j ……X0,J ……………… … …………………
Xi,0 ……Xi,j …… Xi,J = ………………… ……………… … ? XI,0 ……XI,j ……XI,J
C0,0 C0,m C0,M
Cn,0 Cn,m Cn,M
CN,0 CN, CN,M m
Yi,j = Xi-1,j-1 * C n-1,m-1 + X i,j-1* C n,m-1 + X i+1,j-1 * C n+1,m-1
+ X i-1,j * C n-1,m + X i,j * C n,m + X i+1,j * C n+1,m
+ X i-1,j+1 * C n-1,m+1 + X i,j+1 * C n,m+1 + X i+1,j+1 * C n+1,m+1
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Title of Presentation Digital Filters for image processing (2D-FIR)
Blur filter
1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
Sharpening filter
-1 -1 -1 -1 +9 -1 -1 -1 -1
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Digital Filters (IIR)
M ‘FIR’ y[n] a * z −m x[n] + + ∑ m = zY )( = m=0 * zH )( N − a0 zX )( n T ∑bn * z n=0 + + a + * za −1 + a * z −2 zH )( = 0 1 2 * * − −1 − −2 b a 1 1 * zb b2 * z 1 T 1 + * * + b2 a2
• IIR filters: – Have an Infinite Impulse Response – Have relatively low footprint figures (computational load and memory) – Can behave like ‘any’ typical analogue filter (Chebyshev, Butherworth, Bessel, Elliptic, etc) – Can become unstable (like analogue filters)
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Title of Presentation Digital Filters (IIR)
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Quantisation noise
• Noise = actual signal – desired signal
ADC DAC
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Title of Presentation Fixed point Signal to Noise Ratio (SNR)
2 P A = signal = signal Note: for fixed point SNR Pnoise Anoise Dynamic Range (DR) = SNR
P A SNR (dB =10) log signal = 20 log signal 10 10 CD Pnoise Anoise Vinyl
= ()n ≈ • ()Tape SNR (dB ) 20 log 10 2 02.6 n for linear distribute d signals ge .., sawtooth or triangle = ()n ≈ • + SNR (dB ) 20 log 10 2 02.6 n 76.1 ( for sinusoidal signals )
16 bit 12 bit 10 bit 8 bit 6 bit 4 bit SNR 96 dB 72 dB 60 dB 48 dB 36 dB 24 dB Classical Jazz
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Fixed point arithmetics; Q-notation
• Qm.f : s m f – ‘s’ represents sign bit – ‘m’ represents magnitude (= 2 m) – ‘f’ represents fractional part (= 2 -f)
• Q15.0 s 15 bits – signed integer uses 16 bits, resolution is 2 -0 = 1 – ranges between [-215 , 2 -15 - 2-0] = [-32768, +32767] = [0x8000, 0x7FFF]
• Q14.1 s 14 bits 1 b – signed integer uses 16 bits, resolution is 2 -1 = 0.5 – ranges between [-214 , 2 -14 - 2-1] = [-16384.0, +16383.5] = [0x8000, 0x7FFF]
• Q0.15 s 15 bits – signed integer uses 16 bits, resolution is 2 -15 = 0,000030517578125 – ranges between [-20, 2 0 -2-15 ] = [-1, + 0,999969482421875] = [0x8000, 0x7FFF]
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Title of Presentation Fixed point arithmetics
• Adding numbers: ◦ Q15 + Q15 = Q16 ◦ Q15 – Q15 = Q16
• Multiplying numbers: ◦ Q15 * Q15 = Q30 ◦ Q15 / Q15 = Q30 (result + remainder)
• Multiplying by 2 N equals to “ASL
s 1 0 1 0 1 1 0
N • Dividing by 2 equals to “ASR
s s 0 1 0 1 0 1
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Floating point Signal to Noise Ratio (SNR) & Dynamic Range (DR)
IEEE 754 float
IEEE 754 32bit float
SNR = 6.02 * (fraction bits + sign bit) [dB] = 6.02 * 24 bit = 144 [dB] DR = 6.02 * 2 exponent bits [dB] = 6.02 * 2 8 bit = 1536 [dB]
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Title of Presentation Questions
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
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Outline
• Introduction ◦ Definition Digital Signal Processing ◦ Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Title of Presentation Practical exercise 1 : DTMF detection
DTMF = Dual Tone Multi-Frequency DTMF is a system used in telephony to transmit simple commands like phone numbers. The underlying technology is Frequency Shift Keying (FSK). Each command is transmitted by generating two sinusoids (within the speech audio band). E.g. to transmit digit code ‘5’, sinusoids with frequencies of 770Hz and 1336Hz are generated, see table and figure.
1209 Hz 1336 Hz 1477 Hz 1633 Hz 697 Hz 1 2 3 A 770 Hz 4 5 6 B 852 Hz 7 8 9 C 941 Hz * 0 # D
Sequence, e.g. 01-23456789
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Practical exercise 1: approach
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Title of Presentation Practical exercise 1: algorithm
Audio stream
AAudio continuous frame n streamAudio of audioframe samples,.. Audio e.g frame : .. Audio frame2 Audio frame1 - played back from a pre-recorded PC file or -The sampledspectral audio fromstream a liveis dividedspectral audio signalinto frames usingspectral foran analysiADC s purposes:spectral spectral - Framesizeanalysis > N periodsanalysis of the slowestanalysis sinusoid (increaseanalysis SNR) analysis - Framesize < DTMF burst / M (allow multiple detections per DMTF burst) Spectralspectral analysispeak usesspectral Goertzel peak algorithm,spectral and peak is executedspectral once peak for eachspectral peak frequencyevaluation bin (so 8*)evaluation evaluation evaluation evaluation
Peak evaluation: - No peaks detected implies silence between two DTMF bursts DTMF key extraction DTMF key extraction - 2 peaks implies detection of a DTMF key candidate - More than 2 peaks implies too much noise -> invalid DTMF key To prevent false detections, a DTMF key is only valid if multiple DTMF candidates haveDTMF been key detectedconcatenation to extract DTMF string
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Practical exercise 1: goertzel algorithm
Goertzel Detection algorithm: • Efficient spectral analysis implementation to detect single tones, e.g. for DTMF detection. • Is implemented using a high-Q (Notch-like) 2 nd order IIR filter:
• Is more efficient than the Fast Fourier Transform if only a few coefficients are required. • More flexible in choosing the desired time resolution -> ‘N’ (Goertzel block) can have any desired length, • More flexible in choosing the desired center (bin) frequency -> ‘k’ can be any multiple of ‘1/N’
Ones for for every each tone sinusoid & Ones for every tone every sample + +
-1 Coeff1Z Coeff2 + * * Z-1 -1 *
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Title of Presentation Practical exercise 1: create development & test environment
• Development tools for algorithm development ◦ Matlab ◦ Labview ◦ Microsoft .NET (*) ◦ Eclipse with Ansi-C for PC environment ◦ … • Create test vectors ◦ Various *.WAV and *.PCM files with DTMF sequences (10 digits)
• Implement algorithm in floating point arithmetics ◦ For proof of concept of Goertzel and DTMF detection algorithms
• Port algorithm to 32-bit fixed point arithmetics ◦ Quantising & scaling all coefficient and variables ◦ For proof of concept of Goertzel and DTMF detection algorithms in fixed point
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Practical exercise 1: select suitable DSP platform
• Atmel ATmega128; ◦ 8-bit GP-RISC, 16MHz, ◦ 128K FLASH, 4K RAM, 4K EEPROM ◦ 4* (8-bit + 16-bit) Timer/Counter, 8* PWM, 8ch ADC, 2* UART, SPI, WDT, GPIO, JTAG • Microchip dsPIC 33FJ256GP506 (*); ◦ 24i/16d-bit RISC, 40MHz, DSP & C-compiler optimized instruction set ◦ 128k Flash, 16K RAM, 8ch DMA support for memory and peripherals ◦ 9ch timer/counters, 8ch PWM, high speed ADC, 2* SPI, 2* I2C, 2* UART, I2S, CAN, WDT, 53* GPIO, JTAG, nanoWatt features. • Atmel AT32 series; ◦ 32-bit GP-RISC, 33MHz, 43 DMIPS ◦ ≤512K FLASH, ≤64K RAM, DMA support ◦ USB, 10/100 Mbps ethernet, 3ch 16-bit timer/counter, 7ch PWM, I2S, I2C, SPI, 4ch UART, 8ch ADC, 2ch audio DAC, JTAG • Others: ◦ Texas Instruments (TMS320xxx), Analog Devices (Blackfin, Sharc, AD21xxx), Freescale (56xxx), ARMxx, VHDL, etc……
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Title of Presentation Practical exercise 1: why is dsPIC suitable ?
• DSP enabling features: – Modified Harvard architecture (one address bus and two (X/Y) data buses) for single-cycle 3-parameters instructions, e.g. a+b=c – Multiplier supports single cycle 16b*16b = 32b (un)signed MAC (@40Mhz = 25nsec ) – ALU has headroom to allow for multiple accumulates without overflow (40-bit accumulator) – ALU supports automatic saturation (clipping), rounding – Single cycle SHR/SHL
Practical exercise 1: dsPIC prototyping board
• Features – Board includes integrated debugger / programmer – USB powered DM330011 - MPLAB Starter Kit for dsPIC DSC – dsPIC33FJ256GP506 DSC with 256 KB Flash and 16 KB RAM – 16/24/32 bit codec with a maximum sampling frequency of 48KHz – Low cost audio capture and play back circuitry using the 12 bit ADC and PWM Audio – Microphone and line level inputs with adjustable input gain – 100mW headphone amplifier with digital volume control – 2 switches and 3 LEDs for user application purposes – 4 Megabit serial flash memory for application use – Temperature sensor – CD contains MPLAB IDE with full editor, programmer and debugger; MPLAB C Compiler; code examples and user’s guide – All tools provided for developing and prototyping speech and audio application & algorithms
• Package Contents – dsPIC audio board with integrated debugger – MPLAB Starter Kit with CD containing MPLAB IDE, MPLAB C Compiler for dsPIC DSCs, application notes, and sample programs Price € 44 (April 2008) – USB cable
• dsPIC Filter Design (Lite) is sold seperately
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Title of Presentation Practical exercise 1: software ‘design’
Main process Initialisation, UI, …
DSP process • Goertzel processing, Read ADC Write DAC • DTMF key extraction, • DTMF key concatenation
buffer1 buffer3 ADC DAC buffer2 buffer4
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Practical exercise 1: speed optimisation
• Use loop-enrolling to save indexing overhead
for (i=3; i==0; i--) a[0] += b[0] * c[0]; { a[1] += b[1] * c[1]; a[i] += b[i] * c[i]; a[2] += b[2] * c[2]; } a[3] += b[3] * c[3];
• Use built-in functions / macros for a 16b*16b = 32b signed multiply
Q0[0] += (Int16) ( ( (Int32) Coeff[0] * Q1[0]) >> Q14_SCALER); // speed-optimized code using built-in functions Q0[0] += (Int16) (__builtin_mulss(Coeff[0], Q1[0]) >> Q14_SCALER);
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Title of Presentation Practical exercise 1: demo
PIC starter kit
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Questions
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
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Title of Presentation Outline
• Introduction ◦ Definition Digital Signal Processing ◦ Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Practical exercise 2: digital reverb
Reverb A Reverb simulates the component of sound that results from reflections from surrounding walls or objects. It is in effect a room simulator (source: audacity.sourceforge.net).
Speed of sound ≈ 343 m / Sec (at 20 oC) Propagation delay ≈ 3 mSec / m
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Title of Presentation Practical exercise 2: block diagram
Schroeder reverb ‘Dry’ signal Tapped delay
A0 A1 A2 A3
‘Wet’ signal + +
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Practical exercise 2: comb filter
typical K = 30..40 msec
y[n] = x[n] + α * y[n-K]
y[t] 1.0
0.8 0.64 α = 0.8 0.512 0.4 0.33 0.26 0.2
t
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Title of Presentation Practical exercise 2: allpass filter
typical m = 3..5 msec
x(n) q(n) y(n) y(n) = q(n-M) – g * x(n) q(n) = x(n) + g * y(n)
(2nd order all-pass)
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Practical exercise 2: demo
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Title of Presentation Questions
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
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Outline
• Introduction ◦ Definition Digital Signal Processing ◦ Application areas • DSP systems ◦ Analog versus digital ◦ Sensors ◦ AD / DA conversion • DSP theory ◦ Time domain versus frequency domain ◦ Nyquist / Shannon sampling theorem ◦ Digital Filters ◦ Quantisation noise and dynamic range • Practical exercises ◦ DTMF detection ◦ Digital reverb • Further reading
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Title of Presentation Further reading
Literature: • http://www.dspguide.com/pdfbook.htm • http://www.dspguru.com/ • http://www.bores.com • http://www.nl.bol.com/is-bin/INTERSHOP.enfinity/eCS/Store/nl/-/EUR/BOL_DisplayProductInformation- Start?BOL_OWNER_ID=666879353&Section=BOOK Tools: • http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1406&dDocName=en02 3602 • http://www.mathworks.com/products/signal/index.html?s_cid=adw_digitalsp_cat1 • http://www.ni.com/labview/ Platforms: • http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1406&dDocName=en53 4506 • http://www.analog.com/embedded-processing-dsp/processors/en/index.html • http://www.xilinx.com/products/design_resources/dsp_central/grouping/index.htm • http://www.altera.com/technology/dsp/dsp-index.jsp
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Title of Presentation