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I started studying DSP recently. In my MATLAB assignments, I am often asked to plot the frequency response of a digital filter using freqz. I know there's another function for plotting a frequency response, bode.

In my last assignment, I was asked to design a notch filter for $60\textrm{ Hz}$ with a sampling frequency of $200\textrm{ Hz}$. After doing so, I plotted the frequency response using freqz, which gave me the expected result - the notch was on $60\textrm{ Hz}$:

freqz plot

However, when I plot the frequency response using bode, the frequency is off significantly:

enter image description here

To my understanding, both functions measure the frequency response. Why is one giving me the correct result then, when the other is not?

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freqz() plot uses a discrete-time frequency axis, linearly scaled, between $0$ and $1$, ($\times \pi$) radians per sample. For 200 Hz sampling frequency, a 60 Hz notch would be shown at $w_c = 0.6 \pi$ rads, which is put at frequency 0.6.

The Bode-plot, however, uses a logarithmic scale for the continuous-time radian frequency $\Omega$. Given that you have a notch frequency of $60$ Hz, corresponding radian value is $\Omega_c = 2\pi \times 60 \approx 377$ radians per second.

So both plots are showing the notch at the correct place.

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    $\begingroup$ Thank you. I screwed up the conversion from Hz to radians. $\endgroup$
    – Mu3
    May 31, 2017 at 21:47

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