# What are the values on the x-axis when I plot the impulse response of a lowpass filter?

I am trying to develop a filtering routine, using Java, and I am using the windowing method.

From my studies, I was told that if I make a plot of the impulse response of an ideal lowpass filter, I would get a SINC graph. In this situation, what am I plotting against (i.e., what values are on the X-Axis?)?

• The x axis measured in seconds is [0:N-1]/Fs where N is the number of samples in the impulse response and Fs is the sample rate in samples/sec.
– John
Jan 12, 2014 at 23:28

There is a frequency inherent to sinc. Sometimes, the definition is normalized by multiplying $x$ with $\pi$. Then if the sampling frequency of the signal is 1 then, the sampled sinc is identical to a Kronecker delta (that is, a ,,wire'' - it will not filter at all, or identically: a low pass filter with cutoff at Nyquist frequency). In case the cutoff frequency is different, you will need to multiply t by a factor smaller than 1 to get x. Then the factor will be the ratio of cutoff and Nyquist frequency.