# Derivative

## Overview

Discrete-time derivative

## Discussion

Computes the derivative of a discrete-time signal. The derivative is defined as:

\$y[n] = K/T * (x[n] - x[n-1])\$ where T is the sample period and K is the optional gain parameter. The module sets the default starting value to x[-1] = 0.

The discrete derivative is similar to the continuous time derivative. For example, if the input is a sine wave at 1 kHz, then the output will be a cosine at 1 kHz scaled by 2*pi*1000.

The hidden internal array .lastValue stores the previous value x[n-1] between blocks. The length of the array is set by the prebuild function to the number of channels.

## Type Definition

CODE
``````typedef struct _ModuleDerivative
{
ModuleInstanceDescriptor instance;            // Common Audio Weaver module instance structure
FLOAT32* lastValue;                           // Previous value x[n-1].
} ModuleDerivativeClass;``````

## Variables

### Properties

 Name Type Usage isHidden Default value Range Units gain float parameter 0 1 -10:10 linear lastValue float* state 1 [1 x 1] Unrestricted

### Pins

#### Input Pins

Name: in

Description: Input signal

Data type: float

Channel range: Unrestricted

Block size range: Unrestricted

Sample rate range: Unrestricted

Complex support: Real

#### Output Pins

Name: out

Description: Output signal

Data type: float

## MATLAB Usage

File Name: derivative_module.m

CODE
`````` M=derivative_module(NAME)
This module computes the derivative of the input signal.  Mathematically,
this is:
y[n] = 1/dt * (x[n] - x[n-1])
where dt is the time step, dt = 1/SR.  The module has a multichannel
input and computes the derivative per channel.  Arguments:
NAME - name of the module.``````

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