What about all the frequencies in between?

• This filter seems to boost low frequencies while rejecting components at higher frequencies.

• We may find the frequency response of the filter by checking the behaviour of the filter at every possible frequency between 0 and $f_s/2$ Hz (sinewave analysis).

• Alternatively, we can use an input signal that contains all of those frequencies, and then we only have to do the ``checking'' operation once.

• If we use an input signal with the broadest possible spectrum, i.e. an impulse, we will obtain an output from the filter, called an impulse response.

• The impulse response is a time domain description of the filter's response to all frequencies from DC to the Nyquist limit.

• The spectrum of the impulse response gives us the the frequency response of the filter.