Signal Processing Toolbox

Magnitude and Phase

MATLAB provides functions to extract magnitude and phase from a frequency response vector h. The function abs returns the magnitude of the response; angle returns the phase angle in radians. To extract the magnitude and phase of a Butterworth filter:

• [b,a] = butter(6,300/500);
  fvtool(b,a)
  

and then click the Magnitude and Phase Response toolbar button:

The unwrap function is also useful in frequency analysis. unwrap unwraps the phase to make it continuous across 360º phase discontinuities by adding multiples of ±360°, as needed. To see how unwrap is useful, design a 25th-order lowpass FIR filter:

• h = fir1(25,0.4);
  

Obtain the filter's frequency response with freqz, and plot the phase in degrees:

• [H,f] = freqz(h,1,512,2);
  plot(f,angle(H)*180/pi); grid
  
  
  

It is difficult to distinguish the 360° jumps (an artifact of the arctangent function inside angle) from the 180° jumps that signify zeros in the frequency response.

unwrap eliminates the 360° jumps:

• plot(f,unwrap(angle(H))*180/pi);
  

or you can use fvtool to see the unwrapped phase:

• fvtool(b,a)
  
  
  

Analog Domain

Delay