I'm having trouble understanding the frequency normalization of the fir1 function regarding how the units match up.

In my case, I am doing a lab and have to use the fir1 function. What I don't understand is how if my sampling frequency is 44100 samples/second, how is my normalized cutoff frequency of fir1, Wn, between 0 to pi, where pi represents half the sampling rate, but in radians per sample.

To further elaborate, this is kind of a two part question.

1) Why is the normalized frequency between 0 and pi instead of 0 and 2*pi

2) How do the units, samples/second in continuous time go to radians/sample in discrete time.

I hope I was able to elaborate better and can use the help, thanks.

Answer 1

[Star Strider]

1) The 0 to pi range represents the normalised radian representation of the Nyquist frequency, half the sampling frequency. The sampling frequency would normalise in radians to 2*pi.

2) I am not certain tthat I understand this question. The sampling frequency in samples/second normalises to sampling interval (time between samples) in seconds/sample. Note that samples/second is not continuous time and is actually discrete time. (I don't see any reference to radians/sample in my quick review of the fir1 documentation.)