DESC9115 Written Review 2: Digital Implementation of a Leslie Speaker Effect. Digital Audio Systems: DESC9115, Semester

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1 DESC9115 Written Review 2: Digital Implementation of a Leslie Speaker Effect Digital Audio Systems: DESC9115, Semester David Anderson /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 Speaker attempted to mimic the undulating effect of a pipe organ in a acoustic space. Although originally designed for the Hammond organ the Leslie speaker has found many uses in recorded and performed music with Wurlitzer's, guitar and even the human voice. [2] In a typical Leslie speaker the input signal is amplified before being split into its high and low frequency components by a 12dB per octave passive crossover at 800Hz. Once separated, frequencies 800Hz and over are sent to a single rotating horn at the top of the unit (The second horn is used as a counterweight), while frequencies 800Hz and below are sent to a stationary bass driver placed over a rotating baffle. The typical construction of a Leslie speaker can be seen in figure Physical Properties of the Effect The Leslie speaker has a particularly recognizable sonic signature. The Leslie speaker achieves this effect through the Figure 1. Physical Layout of a Leslie Speaker principle of a directional sound source is rotating at constant (or variable) speed simple around a fixed pivot point. [3] Throughout this physical operation two important effects occur at the listening position. The most significant of these is a frequency modulation as the sound source varies in distance from the listener. As the sources rotate towards the listener its relative velocity will increase the pitch of the sound and decrease as it rotates away from the listener. This is the fundamental physical principle the Leslie speaker relies on for its characteristic vibrato effect. This phenomenon is known as the Doppler Effect. The Doppler Effect describes the apparent frequency modulation that occurs when a sound source/ or listener is in motion relative to each other. The second by-product of the rotating sound source is a amplitude modulation. Due to the directional nature of the sound source, the sound intensity fluctuates as the driver rotates facing towards or away from the listener. [4]

2 Another effect present in this analog system is distortions that are introduced by the (originally valve) amplifier circuit. 3. Digital Simulation of the Leslie Speaker - Methods of Simulation Through research into prior digital implementations of the Leslie rotary speaker the author has found two significant methodologies capable of achieving successful emulations of the Leslie speaker system in the digital domain. These are achieved through the use of convolution and FIR filters and alternatively a method using sinusoidally modulated time variant delay lines to approximate the physical effects of the Leslie speaker. In their 2009 paper presented at the 127th AES convention titled Discrete Time Emulation of the Leslie Speaker Jorge 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 amplitude modulations. To recreate the frequency modulation characteristics of the rotary speaker two delay-lines with a phase difference of 180º are modulated with a sinusoidal low frequency oscillator. This process only models the doppler effect characteristic of the Leslie. To simulate the sound intensity differences caused by the directional nature of the speakers the amplitude is modulated with the same LFO used in the delay-line modulation. [5] Left and right signals then need to be combined to a small extent to simulate crosstalk in order to create a believable stereo image. [6] In U. Zozler s text DAFX: Digital Audio Effects a ratio of 0.7 is used for this purpose. It was a simulation of this type that I chose to implement over the course of this unit of study. Code for this implementation can be found in appix 1. Figure 3 - DAFX Leslie Speaker simulation Figure 2 - Discrete time emulation block diagram (Herrera, J et al pp. 3) separately tracked, and used to drive time - variant FIR filters applied to the input. This model s block diagram can be seen in figure 2. In this method the input signal drives a crossover network, which feeds separate timevarying FIR filters, one for the horn, and one for the baffle. The system output is the sum of horn-filtered and baffle-filtered signals. The FIR filters are varied using information gathered from the impulse responses take of each driver. An alternate approach to digital simulations of the Leslie speaker cabinet uses delay line and Figure 3 taken from Zozler s text shows the processing signal flow for a simulation of this type. [7] 4. Range of Parameters of the simulation Best results where achieved from the simulation by constraining parameter values to these present in the original physical system. Values outside of these limits ted to produce effects that where too severe to be considered musical. For the modfreq parameter, which controls the speed of the low frequency oscillator, values varying between 0.5-7Hz produced the best results. These values mimic the rotational speed of the horn in the Leslie speaker cabinet.

3 Variables for the parameter delay produced favorable results with values between and milliseconds. 5. Implementation - Limitations and suggested improvements Over the course of this unit of study I have chosen to implement a Leslie speaker simulation utilizing the delay line modulated by a fixed low frequency oscillator followed by a amplitude modulation using a scaled version of the same LFO. This implementation of a Leslie speaker cabinet is a much simpler process to code than other methods involving convolution, and while valid method does not model the Leslie Speaker as accurately as the convolution and FIR method as it does not take into account a number of factors that have significant tonal impact on the rotary speaker system. One significant flaw in this method of simulation is that it is a broadband process, i.e all frequencies are processed in the same manner. In a actual Leslie speaker cabinet this is certainly not the case. In figure 1 outlining the physical layout of the speaker cabinet this is obvious at for glance. After the entering signal receives amplification it is split into two components and sent to separate drivers for processing, with frequencies above 800Hz processed via the rotating horn at the top of the cabinet and frequencies below 800Hz sent to the stationary speaker with a rotating baffle. This nature of these two speaker systems are significantly important as each impart a distinct sonic characteristic on the signal through which they pass. These sonic characteristics are in part a symptom of the horn and baffles frequency response, both on and off axis. As well as spacial information caused be internal reflections inside the wooden cabinet. modulation effects with little doppler shifting. Frequencies 200Hz and below are essentially unaffected by the rotating baffle due to to having a wavelength much larger than the baffle size. [7] A significant improvement in the delay line model of a Leslie cabinet could be achieved by processing these three key frequency zones indepently. Frequencies above 800Hz would receive processing in a similar manner to the current implementation, but frequencies Hz would receive its delay line processing using a scaled version of the low frequency oscillator to lessen the depth of the doppler shifts in the signal. Frequencies below 200Hz would not receive and delay line or amplitude modulation processing. Another tonal factor not model in this implementation is harmonic distortion present in the system. The valve amplifier in a Leslie cabinet is a fairly significant source of this distortion and is a contributor to a Leslie cabinets characteristic sound. This parameter could be modeled using a subtle tube saturation algorithm utilizing existing models of the harmonic distortion created by triode and tetrode valves that are commonly for in these amplifier circuits. [8] 5. Conclusion The Leslie rotary loudspeaker is an iconic piece of musical equipment, with its sonic signature heavily featuring in contemporary music. By carefully examining and understanding the physical phenomena that occur from this mechanical effect its intrinsic characteristics can be digitally modeled in a pleasing manner. A number of approaches are possible to achieve this and their benefits must be considered in choosing the nature of their application. Another issue of forgoing any frequency depent 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

4 References [1] Vail, Mark (2002). The Hammond Organ - Beauty in The B. Backbeat Books. pp [2][3][7] C. A. Henrickson. Unearthing the Mysteries of the Leslie Cabinet: Recording Engineer/Producer Magazine, April mystery/mystery.html. [4] Serafin, J. O. S. I. S. and Berners, J. A. D 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 [6] Croteau, M Final written review: Development proposal for variable two-way rotary loudspeaker digital audio effect Digital Audio Systems, DESC9115, Semester pp. 2 [8] Baker, B Leslie main amplifier schematic. hammond/faq/files/schematics/122mn-a.pdf

5 Appix 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); L=2+DELAY+WIDTH*2; % Duration of WAV-file in samples % 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 % 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); L = 2+DELAY+WIDTH*2; % Duration of WAV-file in samples % length of the entire delay

6 % 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 % 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 % 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');