DESC9115 Written Review 2: Digital Implementation of a Leslie Speaker Effect

Digital Audio Systems: DESC9115, Semester 1 2014

David Anderson 430476729

06/05/2014

Abstract

In this written review the author discusses the physical properties of a particular audio effect, the Leslie rotary speaker, as well as audio signal processing and DSP techniques required to simulate the effect in the digital domain, comparing existing two methodologies. A implementation performed by the author in then discussed, with improvements suggested.

1. Introduction

The Leslie rotary loudspeaker is an iconic piece of musical equipment. Developed by Donald Leslie the Leslie speaker was first manufactured in 1941 as a add-on accessory to the Hammond Organ. [1] The Leslie Figure 1. Physical Layout of a Leslie Speaker simple Speaker attempted to mimic the undulating effect of a pipe organ in a acoustic space. principle of a directional sound source is Although originally designed for the Hammond rotating at constant (or variable) speed organ the Leslie speaker has found many uses in recorded and performed music with around a fixed pivot point. [3] Throughout this Wurlitzer's, guitar and even the human voice. physical operation two important effects occur [2] at the listening position. The most significant of these is a frequency modulation as the sound In a typical Leslie speaker the input signal is source varies in distance from the listener. As amplified before being split into its high and the sources rotate towards the listener its low frequency components by a 12dB per relative velocity will increase the pitch of the octave passive crossover at 800Hz. Once sound and decrease as it rotates away from separated, frequencies 800Hz and over are the listener. This is the fundamental physical sent to a single rotating horn at the top of the principle the Leslie speaker relies on for its unit (The second horn is used as a characteristic vibrato effect. This phenomenon counterweight), while frequencies 800Hz and is known as the ‘Doppler Effect’. The Doppler below are sent to a stationary bass driver Effect describes the apparent frequency placed over a rotating baffle. The typical modulation that occurs when a sound source/ construction of a Leslie speaker can be seen or listener is in motion relative to each other. in figure 1. The second by-product of the rotating sound source is a amplitude modulation. Due to the 2. Physical Properties of the Effect directional nature of the sound source, the sound intensity fluctuates as the driver rotates The Leslie speaker has a particularly facing towards or away from the listener. [4] recognizable sonic signature. The Leslie speaker achieves this effect through the Another effect present in this analog system is amplitude modulations. To recreate the distortions that are introduced by the (originally frequency modulation characteristics of the valve) amplifier circuit. rotary speaker two delay-lines with a phase difference of 180º are modulated with a 3. Digital Simulation of the Leslie Speaker sinusoidal low frequency oscillator. This - Methods of Simulation process only models the ‘doppler effect characteristic’ of the Leslie. To simulate the Through research into prior digital sound intensity differences caused by the implementations of the Leslie rotary speaker directional nature of the speakers the the author has found two significant amplitude is modulated with the same LFO methodologies capable of achieving used in the delay-line modulation. [5] successful emulations of the Leslie speaker system in the digital domain. These are Left and right signals then need to be achieved through the use of convolution and combined to a small extent to simulate FIR filters and alternatively a method using crosstalk in order to create a believable stereo sinusoidally modulated time variant delay lines image. [6] In U. Zozler’s text DAFX: Digital to approximate the physical effects of the Audio Effects a ratio of 0.7 is used for this Leslie speaker. purpose.

In their 2009 paper presented at the 127th It was a simulation of this type that I chose to AES convention titled ‘Discrete Time implement over the course of this unit of Emulation of the Leslie Speaker’ Jorge study. Code for this implementation can be found in appendix 1. Herrera, Craig Hanson, and Jonathan S. Abel explore a discrete-time emulation of the Leslie speaker acoustics. In which the midrange horn and subwoofer baffle are individually modeled and placed into impulse response matrices, with their rotational dynamics

Figure 3 - DAFX Leslie Speaker simulation

Figure 3 taken from Zozler’s text shows the processing signal flow for a simulation of this Figure 2 - Discrete time emulation block diagram type. [7] (Herrera, J et al pp. 3) 4. Range of Parameters of the simulation separately tracked, and used to drive time - variant FIR filters applied to the input. This Best results where achieved from the model’s block diagram can be seen in figure 2. simulation by constraining parameter values to In this method the input signal drives a these present in the original physical system. crossover network, which feeds separate time- Values outside of these limits tended to varying FIR filters, one for the horn, and one produce effects that where too severe to be for the baffle. The system output is the sum of considered musical. For the ‘modfreq’ horn-filtered and baffle-filtered signals. The parameter, which controls the speed of the low FIR filters are varied using information frequency oscillator, values varying between gathered from the impulse responses take of 0.5 - 7Hz produced the best results. These each driver. values mimic the rotational speed of the horn in the Leslie speaker cabinet. An alternate approach to digital simulations of the Leslie speaker cabinet uses delay line and Variables for the parameter ‘delay’ produced modulation effects with little doppler shifting. favorable results with values between 0.001 Frequencies 200Hz and below are essentially and 0.005 milliseconds. unaffected by the rotating baffle due to to having a wavelength much larger than the 5. Implementation - Limitations and baffle size. [7] suggested improvements A significant improvement in the delay line Over the course of this unit of study I have model of a Leslie cabinet could be achieved by chosen to implement a Leslie speaker processing these three key frequency zones simulation utilizing the delay line modulated by independently. Frequencies above 800Hz a fixed low frequency oscillator followed by a would receive processing in a similar manner amplitude modulation using a scaled version of to the current implementation, but frequencies the same LFO. 200 - 800Hz would receive its delay line processing using a scaled version of the low This implementation of a Leslie speaker frequency oscillator to lessen the depth of the cabinet is a much simpler process to code doppler shifts in the signal. Frequencies below than other methods involving convolution, and 200Hz would not receive and delay line or while valid method does not model the Leslie amplitude modulation processing. Speaker as accurately as the convolution and FIR method as it does not take into account a Another tonal factor not model in this number of factors that have significant tonal implementation is harmonic distortion present impact on the rotary speaker system. in the system. The valve amplifier in a Leslie cabinet is a fairly significant source of this One significant flaw in this method of distortion and is a contributor to a Leslie simulation is that it is a broadband process, i.e cabinets characteristic sound. This parameter all frequencies are processed in the same could be modeled using a subtle tube manner. In a actual Leslie speaker cabinet this saturation algorithm utilizing existing models of is certainly not the case. In figure 1 outlining the harmonic distortion created by triode and the physical layout of the speaker cabinet this tetrode valves that are commonly for in these is obvious at for glance. After the entering amplifier circuits. [8] signal receives amplification it is split into two components and sent to separate drivers for 5. Conclusion processing, with frequencies above 800Hz processed via the rotating horn at the top of The Leslie rotary loudspeaker is an iconic the cabinet and frequencies below 800Hz sent piece of musical equipment, with its sonic to the stationary speaker with a rotating baffle. signature heavily featuring in contemporary This nature of these two speaker systems are music. By carefully examining and significantly important as each impart a distinct understanding the physical phenomena that sonic characteristic on the signal through occur from this mechanical effect its intrinsic which they pass. These sonic characteristics characteristics can be digitally modeled in a are in part a symptom of the horn and baffles pleasing manner. A number of approaches are frequency response, both on and off axis. As possible to achieve this and their benefits must well as spacial information caused be internal be considered in choosing the nature of their reflections inside the wooden cabinet. application.

Another issue of forgoing any frequency dependent processing is evident in the way the emulation handles low frequency content. In this digital emulation low frequencies are affected by the process to the same effect as higher frequencies, down to DC. In the physical system this does not only not occur but is physically impossible using speaker and baffle sizes seen in typical Leslie cabinets. In a physical Leslie cabinet frequencies processed by the rotating baffle exhibit mostly amplitude References

[1] Vail, Mark (2002). The Hammond Organ - Beauty in The B. Backbeat Books. pp. 129– 131

[2][3][7] C. A. Henrickson. Unearthing the Mysteries of the Leslie Cabinet: Recording Engineer/Producer Magazine, April 1981. http://theatreorgans.com/hammond/faq/ mystery/mystery.html.

[4] Serafin, J. O. S. I. S. and Berners, J. A. D. 2006. Doppler Simulation and the Leslie. pp. 3

[5][7] U. Zolzer, “modulators and demodulators,” in DAFX: Digital Audio Effects, England, West Sussex: JW & Sons, 2002, pp. 86 – 88.

[6] Croteau, M. 2012. ‘Final written review: Development proposal for variable two-way rotary loudspeaker digital audio effect’ Digital Audio Systems, DESC9115, Semester 1 2012 pp. 2

[8] Baker, B. 1995. 122 Leslie main amplifier schematic. http://theatreorgans.com/ hammond/faq/files/schematics/122mn-a.pdf Appendix 1 - Leslie speaker simulation MATLAB Code function [ output ] = lesliespeaker( audioin , fs, modfreq, delay) %DSP implementation of a rotary speaker effect

[samples channels] = size(audioin); % Determines channel count of input file if channels == 1; % mono processing

processmono = audioin;

DELAY = round(delay*fs); % intial delay in # samples WIDTH = round(delay*fs); % modulation width in # samples

MODFREQ = modfreq/fs; % modulation frequency in # samples

Dur = length(audioin); % Duration of WAV-file in samples

L=2+DELAY+WIDTH*2; % length of the entire delay

DelaylineM =zeros(L,1); % memory allocation for delay DelayOutM = zeros(size(processmono));

for n=1:(Dur-1)

M = MODFREQ;

LFO = 0.5.*sin(M*2*pi*n); %function for delay modulation

ZEIGER = 1+DELAY+WIDTH*LFO;

i = floor(ZEIGER);

frac = ZEIGER-i;

DelaylineM =[processmono(n);DelaylineM(1:L-1)];

DelayOutM(n,1)=DelaylineM(i+1)*frac+DelaylineM(i)*(1-frac); %Linear Interpolation end

% Amplitude modulation of the delayline output

AmpModM = DelayOutM .* LFO;

output = AmpModM;

output = output./max(abs(output(:)))*(1-(2^-(16-1))); %normailize

elseif channels == 2; % stereo processing

processLeft = audioin(:,1); % isolating left channel as variable processRight = audioin(:,2); % isolating right channel as variable

DELAY = round(delay*fs); % intial delay in # samples WIDTH = round(delay*fs); % modulation width in # samples

MODFREQ = modfreq/fs; % modulation frequency in # samples

Dur = length(audioin); % Duration of WAV-file in samples

L = 2+DELAY+WIDTH*2; % length of the entire delay

% Delay line left Channel

DelaylineL = zeros(L,1); % memory allocation for delay array DelayOutL = zeros(size(processLeft));% memory allocation for delay output for n = 1:(Dur-1)

M = MODFREQ;

LFO = 0.5.*sin(M*2*pi*n); %function for delay modulation

ZEIGER = 1+DELAY+WIDTH*LFO;

i = floor(ZEIGER);

frac = ZEIGER-i;

DelaylineL =[processLeft(n);DelaylineL(1:L-1)];

DelayOutL(n,1)=DelaylineL(i+1)*frac+DelaylineL(i)*(1-frac); %Linear Interpolation end

% Delay line right Channel

DelaylineR = zeros(L,1); % memory allocation for delay array DelayOutR = zeros(size(processRight));

for n=1:(Dur-1)

M = MODFREQ;

LFO = -0.5.*sin(M*2*pi*n); %function for delay and amplitude modulation (low frequency oscillator)

ZEIGER = 1+DELAY+WIDTH*-LFO;

i = floor(ZEIGER);

frac = ZEIGER-i;

DelaylineR = [processRight(n);DelaylineR(1:L-1)];

DelayOutR(n,1)=DelaylineR(i+1)*frac+DelaylineR(i)*(1-frac); %Linear Interpolation end

% Amplitude modulation of the delayline output

AmpModL = DelayOutL .* 0.4*LFO; AmpModR = DelayOutR .* 0.4*-LFO;

% simulating crosstalk

EffectOutL = AmpModL + (AmpModR.*0.7); EffectOutR = AmpModR + (AmpModL.*0.7);

output = [EffectOutL, EffectOutR]; %combining channels as a stereo file

output = output./max(abs(output(:)))*(1-(2^-(16-1))); %normailize else error('this function is only a mono or stereo effect'); end