# FREQS

## Purpose:

Evaluates the frequency response of a Laplace transform.

## Syntax:

FREQS(b, a, N)

(h,w ) = FREQS(b, a, N)

 b - A series. The numerator (i.e. zero) coefficients. a - A series. The denominator (i.e. pole) coefficients. N - Optional. An integer, the number of output samples, defaults to 200.

## Alternate Syntax:

FREQS(b, a, w)

(h, w) = FREQS(b, a, w)

 b - A series. The numerator (i.e. zero) coefficients. a - A series. The denominator (i.e. pole) coefficients. w - A series. The angular frequencies in radians/s to evaluate the system.

## Returns:

Displays the magnitude and phase response in two Windows.

h = FREQS(b, a) returns the complex frequency response as one XY series.

(h, w) = FREQS(b, a) returns the complex frequency response as two separate series.

## Example:

h = freqs({1}, {1, -0.5, 0.2})

h contains 200 samples of the frequency response of the continuous system: The angular frequency values range from 0 to 10 radians/s.

## Example:

freqs({1}, {1, -0.5, 0.2}, 1024)

Returns 1024 samples of the magnitude and phase response of the system in two separate Windows:

## Example:

b = {0.2, 0.3, 1.0}

a = {1.0, 0.4, 1.0}

w = logspace(-1, 1)

freqs(b, a, w) Displays 100 samples of the magnitude and phase response of the system: ## Remarks:

FREQS displays the magnitude and phase response of the continuous system specified by the Laplace transform: s = jω complex frequency N = number of numerator terms M = number of denominator terms

If no output arguments are provided, the magnitude and phase response are displayed in two separate windows.

The angular frequency values ω, are in radians/s where ω = 2πf.

See SFREQ to display a continuous complex frequency response with frequency values in Hertz.

FREQS(b, a) or FREQS(b, a, N) automatically chooses frequencies to best capture the magnitude characteristics of the system

FREQS(b, a, w) where w is a series, computes the frequency response at each frequency sample of w.

FILTEQ

FREQZ

INVFREQS

INVFREQZ

MAGNITUDE

PHASE

RESIDUE

RESIDUEZ

SFREQ

SPLANE

ZFREQ