Recall from (Reference) that the convolution integral

has the Fourier Transform:

where *frequency response*:

The frequency response, the Fourier Transform of the impulse response of a filter, is useful since it gives a highly descriptive representation of the properties of the filter. The frequency response can be considered to be the *gain* of the filter, expressed as a function of frequency. The magnitude of the frequency response evaluated at *lowpass* filter is a filter which only passes low frequencies, while *attenuating* or filtering out higher frequencies. A *highpass* filter would do just the opposite, it would filter out low frequencies and allow high frequencies to pass. Figure 1 shows examples of these various filter types.