Ideal HighPass Filter Impulse Response

How to Use the Calculator

1. Enter the Cutoff Frequency in Hertz (Hz). This is the frequency above which signals will pass through the filter.
2. Enter the Sampling Rate in Hertz (Hz). This is the number of samples per second taken from the input signal.
3. Specify the Impulse Duration in seconds. This determines how long the impulse signal lasts.
4. Click the Calculate button to compute the impulse response.
5. The calculator will display the impulse response values and the formula used for calculation.

Working Principle

An ideal high-pass filter passes signals with frequencies higher than a certain cutoff frequency and attenuates signals with lower frequencies. The impulse response of an ideal high-pass filter is the output signal when the input is an impulse signal (a signal that is 1 at one point and 0 elsewhere).

The formula used for the ideal high-pass filter impulse response is:

h[n] = sinc((n - N/2) * (f_c / f_s))

where:

• n is the sample index
• N is the number of samples in the impulse duration
• f_c is the cutoff frequency
• f_s is the sampling rate
• sinc(x) = sin(πx) / (πx) is the sinc function

The sinc function has a central peak at n = N/2 and oscillates with decreasing amplitude as n moves away from N/2. The width of the main lobe of the sinc function determines the transition bandwidth of the filter.