07_CM0268_DSP - Basic Digital Audio Signal Processing In...

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CM0268 MATLAB DSP GRAPHICS 1 174 JJ II J I Back Close Basic Digital Audio Signal Processing In this section we look at some basic aspects of Digital Audio Signal Processing: Some basic definitions and principles Filtering Basic Digital Audio Effects
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CM0268 MATLAB DSP GRAPHICS 1 175 JJ II J I Back Close Simple Waveforms Frequency is the number of cycles per second and is measured in Hertz (Hz) Wavelength is inversely proportional to frequency i.e. Wavelength varies as 1 frequency
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CM0268 MATLAB DSP GRAPHICS 1 176 JJ II J I Back Close The Sine Wave and Sound The general form of the sine wave we shall use (quite a lot of) is as follows: y = A.sin (2 π.n.F w /F s ) where: A is the amplitude of the wave, F w is the frequency of the wave, F s is the sample frequency, n is the sample index. MATLAB function: sin() used — works in radians
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CM0268 MATLAB DSP GRAPHICS 1 177 JJ II J I Back Close MATLAB Sine Wave Radian Frequency Period Basic 1 period Simple Sine wave — 1 period is 2 π radians % Basic 1 period Simple Sine wave i=0:0.2:2 * pi; y = sin(i); figure(1) plot(y); % use stem(y) as alternative plot as in lecture notes to % see sample values title(’Simple 1 Period Sine Wave’);
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CM0268 MATLAB DSP GRAPHICS 1 178 JJ II J I Back Close MATLAB Sine Wave Amplitude Sine Wave Amplitude is -1 to +1. To change amplitude multiply by some gain ( amp ): % Now Change amplitude amp = 2.0; y = amp * sin(i); figure(2) plot(y); title(’Simple 1 Period Sine Wave Modified Amplitude’);
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CM0268 MATLAB DSP GRAPHICS 1 179 JJ II J I Back Close MATLAB Sine Wave Frequency % Natural frequency is 2 * pi radians % If sample rate is F_s HZ then 1 HZ is 2 * pi/F_s % If wave frequency is F_w then freequency is F_w * (2 * pi/F_s) % set n samples steps up to sum duration nsec * F_s where nsec is the % duration in seconds % So we get y = amp * sin(2 * pi * n * F_w/F_s); F_s = 11025; F_w = 440; nsec = 2; dur= nsec * F_s; n = 0:dur; y = amp * sin(2 * pi * n * F_w/F_s); figure(3) plot(y(1:500)); title(’N second Duration Sine Wave’);
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CM0268 MATLAB DSP GRAPHICS 1 180 JJ II J I Back Close MATLAB Sine Wave Plot of n cycles % To plot n cycles of a waveform ncyc = 2; n=0:floor(ncyc * F_s/F_w); y = amp * sin(2 * pi * n * F_w/F_s); figure(4) plot(y); title(’N Cycle Duration Sine Wave’);
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CM0268 MATLAB DSP GRAPHICS 1 181 JJ II J I Back Close Cosine, Square and Sawtooth Waveforms MATLAB functions cos() (cosine), square() and sawtooth() similar.
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CM0268 MATLAB DSP GRAPHICS 1 182 JJ II J I Back Close MATLAB Cos v Sin Wave % Cosine is same as Sine (except 90 degrees out of phase) yc = amp * cos(2 * pi * n * F_w/F_s); figure(5); hold on plot(yc,’b’); plot(y,’r’); title(’Cos (Blue)/Sin (Red) Plot (Note Phase Difference)’); hold off;
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CM0268 MATLAB DSP GRAPHICS 1 183 JJ II J I Back Close Relationship Between Amplitude, Frequency and Phase
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CM0268 MATLAB DSP GRAPHICS 1 184 JJ II J I Back Close Amplitudes of a Sine Wave % Simple Sin Amplitude Demo samp_freq = 400; dur = 800; % 2 seconds amp = 1; phase = 0; freq = 1; s1 = mysin(amp,freq,phase,dur,samp_freq); axisx = (1:dur) * 360/samp_freq; % x axis in degrees plot(axisx,s1); set(gca,’XTick’,[0:90:axisx(end)]); fprintf(’Initial Wave: \t Amplitude = . ..\n’, amp, freq, phase,. ..); % change amplitude amp = input(’\nEnter Ampltude:\n\n’);
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This note was uploaded on 01/24/2012 for the course CM 0268 taught by Professor Davidmarshall during the Winter '11 term at Cardiff University.

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07_CM0268_DSP - Basic Digital Audio Signal Processing In...

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