Frequency and Impulse Response of Linear Filters

ω

c

0

ω

o

0

filter type

lowpass filter

highpass filter

bandpass filter

This Demonstration shows the relationship between the impulse response and the frequency response for ideal lowpass, bandpass, and highpass filters.

Snapshot 1: lowpass filter, with the cutoff frequency

ω

c

=1rad

Snapshot 2: highpass filter, with the cutoff frequency

ω

c

=1rad

Snapshot 3: bandpass filter, centered at frequency

ω

0

=2rad

and with width

2

ω

c

=1rad

For the lowpass and highpass filters, you specify the cutoff frequency

ω

c

; for the bandpass filter, you specify the frequency that the passband is centered about

ω

0

and the width of the passband

ω

c

. Changing

ω

0

for the lowpass or highpass filters has no effect on the system, so the slider is disabled in those cases.

Vincent Tjeng