Homework assignment: make a bode plot of the convolution filters [1 1 1] vs [1 2 1].
Which one turns +1, -1, +1, -1, .. into all zeroes?
You ought to know this because the fourier transform of [1 0 1] is a cosine of amplitude 2 on the complex unit circle e^(i*omega), which means the DC quefrency needs to be 2 to get the zeroes to end up at nyquist.
The frequency response H(z) (= H(e^i*omega)) of [1 1 1] on the other hand will have its minimum somewhere in the middle.
Also here's a post that will teach you how to sight read the frequency response of symmetric FIR filters off the coefficients:
https://acko.net/blog/stable-fiddusion/
Which one turns +1, -1, +1, -1, .. into all zeroes?
You ought to know this because the fourier transform of [1 0 1] is a cosine of amplitude 2 on the complex unit circle e^(i*omega), which means the DC quefrency needs to be 2 to get the zeroes to end up at nyquist.
The frequency response H(z) (= H(e^i*omega)) of [1 1 1] on the other hand will have its minimum somewhere in the middle.
Also here's a post that will teach you how to sight read the frequency response of symmetric FIR filters off the coefficients: https://acko.net/blog/stable-fiddusion/