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- 19th August 2007, 14:53 #1

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## derivative of step response

Hello,

Can anyone tell me what is the different between Step response and impulse response in DSP? Thanks.

- 19th August 2007, 14:53

- 19th August 2007, 15:49 #2

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## step 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.

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- 19th August 2007, 15:49

- 19th August 2007, 17:00 #3

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## step response in dsp

step response denotes the response of the system to a input step signal and this includes a lot of parameters like damping coeff, settling time, etc etc.... impulse response is the response of a system to a input impulse signal... actually an perfect impulse cannot be generated and hence it is found by using the closest approx of impulse signal possible....

- 19th August 2007, 17:00

- 20th August 2007, 02:48 #4

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## step response of a system

Hello artsil23,

The thing i don't understand here is how to convert the impulse response to the step response. In your reply, you are saying we use the derivative to do it.

Do you have any example or formula that related to the derivative? Thanks.

- 20th August 2007, 04:41 #5

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## dsp impulse response

- 20th August 2007, 12:52 #6

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## step response +derivative

Impulse response is the system's reaction for Dirac's input impulse (delta-function) bwith initial zero conditions. In practice it's usually defined by the use of rectangular input impulse, which has too little duration. If you know the impulse response of the system and the input signal as well you may evaluate the output one (the reaction of the system).

Step response is the output for Heaviside function with zero init6ial conditions too. Step response is less practically useful than the impulse one, however it's much easily to define it, as you see.

Besides, Dirac impulse is the derivative of the Heaviside function, therefore if the system is linear (it means that superposition principle is fair) you may just differentiate the step reponse in order to find the impulse one.

Another thing is that impulse response may be evaluated through the Fourier transform of Frequency characteristics (if it's known, of course).

With respect,

Dmitrij

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