# IMPS

## Purpose:

Calculates the impulse response of a Laplace transform.

## Syntax:

IMPS(b, a, t)

(h, t) = IMPS(b, a, t)

 b - A series. The numerator (i.e. zero) coefficients in descending powers of s. a - A series. The denominator (i.e. pole) coefficients in descending powers of s t - Optional. A series or integer, the time values. If an integer or not specified, the time duration is computed based on the exponential time constant and t values are returned where t defaults to 512. If a series, the t values are used directly.

## Returns:

An XY series, the impulse response of the system.

(h, t) = IMPS(b, a, t) returns the impulse response and time values as two separate series.

## Example:

Given: W1: imps({1}, {1, 0.5})

W1 contains 512 samples of the series h(t) = e-0.5t.

## Example:

Given: representing the partial fraction expansion: The impulse response for t >= 0 can be found by inspection: W1: imps({1}, {1, 4, 3})

W2: -0.5 * exp(-3*xvals(w1)) + 0.5 * exp(-xvals(w1))

W3: w1 - w2

W1 displays 512 samples of the calculated response.

W2 contains 512 samples of the analytical impulse response using the same time values as W1.

W3 confirms that the difference is negligible.

## Remarks:

Given the rational polynomial H(s) = b(s) / a(s) where: s = jω complex frequency N = number of numerator terms M = number of denominator terms

The impulse response is calculated from the partial fraction expansion of the system equation.

If there are no output arguments, the result is displayed in the current window.