x(t) = | cos(2πft)|, f != 0

is the input of an ideal band-pass filter with bandwidth B = 3f/2. How can i Find the Output of the y(t) of the signal.

  • 1
    $\begingroup$ You can't, unless you also know the center frequency of the BP filter. By the way, this sounds like homework, which is OK, but in this case it's appreciated if you show your own effort and where you're stuck. $\endgroup$
    – Matt L.
    Commented Feb 4, 2015 at 21:19
  • $\begingroup$ If it were a low-pass filter, the answer would be $0$. $\endgroup$
    – Matt L.
    Commented Feb 4, 2015 at 21:20

1 Answer 1


Your signal is periodic with period $\frac{1}{2f}$ hence has a Fourier series expansion with spacing between the frequency components of $2f$. The output of your ideal filter then is the sum of the Fourier components that fall within the bandwidth.

Because your bandwidth is less than the spacing between the frequency components your output will contain at most one frequency component.


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