Engineering Math

Step vs Impulse Response

When you apply a step function to your system, then you will get the step response. In you apply the derivative to this step response, then you obtain the impulse response, and then take the FFT of the impulse response to obtain the frequency response of the system.

In another words. Impulse response is a quick way to measure the frequency response of a device. Because an impulse in the time domain is equivalent to all frequencies of a sine wave in the frequency domain, we can use an impulse as an input to derive the frequency response. In this case, you measure the effect of sine waves at all frequencies at one time. To use the impulse response method, you input an impulse into the system and measure the output. Then you take the output measurement and apply a Fast Fourier Transform (FFT). The result is the frequency response of the system.

Because creating an impulse is difficult in the real word, finding the impulse response of a device is very difficult. However, using the step response method you can derive the impulse response. The basis of the step response method is that the derivative of a step function is an impulse; the vertical portion of the step function has an infinite derivative. To use the step response method, input a step pattern with a fast rising edge (a slow square wave, 1 kHz will do) into the system. Next, measure the output waveform and take the derivative. The result is the impulse response of the device. Now you can apply the FFT to the impulse response and obtain the frequency response.