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 gain;                                 // Additional gain.
    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.