MATLAB: Phase Shift Sawtooth Wave

function generatorMATLABphase shiftplotpulsesawtoothtrianglewave

Hi everyone,

I am trying to plot a triangular wave for a specified time using the sawtooth function in Matlab. The user inputs values for T_amp, T_freq, and ft and the code then calculates the sawtooth and plots the function vs time, ft.

When plotted, the plot shows the sawtooth starting at -T_amp. I was wondering if there was a way to shift the function so that the sawtooth starts at 0, where the first point would be (0,0) instead of (0, -T_amp). If anyone could help me out with this, I would really appreciate it. Thanks!

tri = T_amp*sawtooth(T_freq*ft, .5);
plot(ft, tri;)

Best Answer

The sawtooth function does not automatically account for the 2*pi required to plot with frequency. To add a phase shift, you can do the same as if it were a sign wave by adding or subtracting your phase:

tri = sawtooth(2*pi*T_freq*ft+(pi/2), .5);

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MATLAB: Incorrect phase from fourier transform

Hi Nathan,

If you check you will see that the difference between random_phase and phase is always either 0 or 2pi. This is because random_phase is constructed so that 0 <= random_phase <= 2*pi, whereas the output of the angle function has -pi < angle <= pi. When random_phase is between 0 and pi things agree, and when random_phase is between pi and 2pi then there is a difference of 2pi between that and the angle function.

If you define random_phase such that -pi <= random_phase <= pi, you'll always get agreement.

MATLAB: Regarding phase compensation

I understand that you are trying to do phase compensation. Please note that a shift in time domain is equivalent to multiplication in frequency domain.

The value of 'theta_estimate" seems to be accurate.

However, one way to perform phase synchronization is to take the Fourier transform of the signal s2, and store it in S2. In the frequency domain, we can multiply S2 with exp(-theta_estimate*i/length(S2)). This is equivalent to shifting the phase of s2 by theta_estimate. We can then obtain the inverse Fourier transform of this product.

Please refer to the following code snippet:

      theta = pi/5; 
      fs = 1000;
      t=(0:1000)/fs;
      freq = 20;
      s1 = sin(2*pi*freq*t);
      s2 = sin(2*pi*freq*t + theta);
      theta_estimate = acos( 2*mean( s1.*s2) );
      %Calculate fft of s2
      S2 = fft(s2);
     % Multiplication in frequency domain means, shift by "theta_estimate" in time domain. This will  
     % subtract "theta_estimate" from s2. 
      S3 = S2.*exp(-i*theta_estimate/(length(S2)));
      % Take inverse fft to get signal in time domain
      s3p = ifft(S3);
      %Calculate the time shift
      time_shift_num = theta_estimate/(2*pi*freq)
      % Plot both the signals
      figure
      plot(t,s1,'r*') 
      hold on
      plot(t+time_shift_num,real(s3p),'b--')

The plots should not have phase shift between them now.

Best Answer

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MATLAB: Incorrect phase from fourier transform

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