Filtering Functions

Modules
	High Precision Q31 Biquad Cascade Filter
	This function implements a high precision Biquad cascade filter which operates on Q31 data values. The filter coefficients are in 1.31 format and the state variables are in 1.63 format. The double precision state variables reduce quantization noise in the filter and provide a cleaner output. These filters are particularly useful when implementing filters in which the singularities are close to the unit circle. This is common for low pass or high pass filters with very low cutoff frequencies.
	Biquad Cascade IIR Filters Using Direct Form I Structure
	This set of functions implements arbitrary order recursive (IIR) filters. The filters are implemented as a cascade of second order Biquad sections. The functions support Q15, Q31 and floating-point data types. Fast version of Q15 and Q31 also available.
	Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
	This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure. The filters are implemented as a cascade of second order Biquad sections. These functions provide a slight memory savings as compared to the direct form I Biquad filter functions. Only floating-point data is supported.
	Convolution
	Convolution is a mathematical operation that operates on two finite length vectors to generate a finite length output vector. Convolution is similar to correlation and is frequently used in filtering and data analysis. The NMSIS DSP library contains functions for convolving Q7, Q15, Q31, and floating-point data types. The library also provides fast versions of the Q15 and Q31 functions.
	Partial Convolution
	Partial Convolution is equivalent to Convolution except that a subset of the output samples is generated. Each function has two additional arguments. firstIndex specifies the starting index of the subset of output samples. numPoints is the number of output samples to compute. The function computes the output in the range [firstIndex, ..., firstIndex+numPoints-1]. The output array pDst contains numPoints values.
	Correlation
	Correlation is a mathematical operation that is similar to convolution. As with convolution, correlation uses two signals to produce a third signal. The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution. Correlation is commonly used to measure the similarity between two signals. It has applications in pattern recognition, cryptanalysis, and searching. The NMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types. Fast versions of the Q15 and Q31 functions are also provided.
	Finite Impulse Response (FIR) Decimator
	These functions combine an FIR filter together with a decimator. They are used in multirate systems for reducing the sample rate of a signal without introducing aliasing distortion. Conceptually, the functions are equivalent to the block diagram below:
	Finite Impulse Response (FIR) Filters
	This set of functions implements Finite Impulse Response (FIR) filters for Q7, Q15, Q31, and floating-point data types. Fast versions of Q15 and Q31 are also provided. The functions operate on blocks of input and output data and each call to the function processes blockSize samples through the filter. pSrc and pDst points to input and output arrays containing blockSize values.
	Finite Impulse Response (FIR) Lattice Filters
	Finite Impulse Response (FIR) Sparse Filters
	Infinite Impulse Response (IIR) Lattice Filters
	This set of functions implements lattice filters for Q15, Q31 and floating-point data types. Lattice filters are used in a variety of adaptive filter applications. The filter structure has feedforward and feedback components and the net impulse response is infinite length. The functions operate on blocks of input and output data and each call to the function processes blockSize samples through the filter. pSrc and pDst point to input and output arrays containing blockSize values.
	Levinson Durbin Algorithm
	Least Mean Square (LMS) Filters
	LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions. LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal. Adaptive filters are often used in communication systems, equalizers, and noise removal. The NMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types. The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.
	Normalized LMS Filters
	This set of functions implements a commonly used adaptive filter. It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization factor which increases the adaptation rate of the filter. The NMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.
	Finite Impulse Response (FIR) Interpolator
	These functions combine an upsampler (zero stuffer) and an FIR filter. They are used in multirate systems for increasing the sample rate of a signal without introducing high frequency images. Conceptually, the functions are equivalent to the block diagram below:

Detailed Description