# Function freqz #

Calculates the frequency response of a filter given its numerator and denominator coefficients.

## Syntax #

``````math.freqz(b, a)
math.freqz(b, a, w)
``````

### Parameters #

Parameter Type Description
`b` Array.<number> The numerator coefficients of the filter.
`a` Array.<number> The denominator coefficients of the filter.
`w` Array.<number> A vector of frequencies (in radians/sample) at which the frequency response is to be computed or the number of points to compute (if a number is not provided, the default is 512 points)

### Returns #

Type Description
Object An object with two properties: h, a vector containing the complex frequency response, and w, a vector containing the normalized frequencies (in radians/sample) at which the response was computed.

### Throws #

Type | Description —- | ———–

## Examples #

``````math.freqz([1, 2], [1, 2, 3], 4) // returns { h: [0.5 + 0i, 0.4768589245763655 + 0.2861153547458193i, 0.25000000000000006 + 0.75i, -0.770976571635189 + 0.4625859429811135i], w: [0, 0.7853981633974483, 1.5707963267948966, 2.356194490192345 ] }
math.freqz([1, 2], [1, 2, 3], [0, 1]) // returns { h: [0.5 + 0i, 0.45436781 + 0.38598051i], w: [0, 1] }
``````