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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 2 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 3 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 . 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 4 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 5 Digital Signal Processing – application fields Sensor signal processing is still hot & high tech 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 6 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 7 Digital Signal Processing – application examples Etc, etc, etc 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 8 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 9 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) 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 10 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 11 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) 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 12 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 14 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 15 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 16 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 17 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 18 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 19 Time domain versus frequency domain N = ω +ϕ f() t ∑ An *sin( n *t n ) = n=1 + = ω +ϕ f() t 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 ) 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 20 Title of Presentation Time domain versus frequency domain • Test signal • Music 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 21 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 * 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 22 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 23 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 24 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 25 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 = Y() z = −n H() z ∑ an * z X() z n=0 = + −1 + −2 + −3 +K+ −M • FIR filters: H() z 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 26 Title of Presentation Digital Filters (FIR) 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No. 27 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 16 May 2010 An introduction to Digital Signal Processing – Felix Donkers No.