Modules

Here is a list of all modules:

[detail level 123]

►Basic Math Functions
Vector Absolute Value	Computes the absolute value of a vector on an element-by-element basis
Vector Addition	Element-by-element addition of two vectors
Vector bitwise AND	Compute the logical bitwise AND
Elementwise clipping	Element-by-element clipping of a value
Vector Dot Product	Computes the dot product of two vectors. The vectors are multiplied element-by-element and then summed
Vector Multiplication	Element-by-element multiplication of two vectors
Vector Negate	Negates the elements of a vector
Vector bitwise NOT	Compute the logical bitwise NOT
Vector Offset	Adds a constant offset to each element of a vector
Vector bitwise inclusive OR	Compute the logical bitwise OR
Vector Scale	Multiply a vector by a scalar value. For floating-point data, the algorithm used is:
Vector Shift	Shifts the elements of a fixed-point vector by a specified number of bits. There are separate functions for Q7, Q15, and Q31 data types. The underlying algorithm used is:
Vector Subtraction	Element-by-element subtraction of two vectors
Vector bitwise exclusive OR	Compute the logical bitwise XOR
Bayesian estimators	Implement the naive gaussian Bayes estimator. The training must be done from scikit-learn
►Complex Math Functions	This set of functions operates on complex data vectors. The data in the complex arrays is stored in an interleaved fashion (real, imag, real, imag, ...). In the API functions, the number of samples in a complex array refers to the number of complex values; the array contains twice this number of real values
Complex Conjugate	Conjugates the elements of a complex data vector
Complex Dot Product	Computes the dot product of two complex vectors. The vectors are multiplied element-by-element and then summed
Complex Magnitude	Computes the magnitude of the elements of a complex data vector
Complex Magnitude Squared	Computes the magnitude squared of the elements of a complex data vector
Complex-by-Complex Multiplication	Multiplies a complex vector by another complex vector and generates a complex result. The data in the complex arrays is stored in an interleaved fashion (real, imag, real, imag, ...). The parameter numSamples represents the number of complex samples processed. The complex arrays have a total of 2*numSamples real values
Complex-by-Real Multiplication	Multiplies a complex vector by a real vector and generates a complex result. The data in the complex arrays is stored in an interleaved fashion (real, imag, real, imag, ...). The parameter numSamples represents the number of complex samples processed. The complex arrays have a total of 2*numSamples real values while the real array has a total of numSamples real values
►Controller Functions
Sine Cosine	Computes the trigonometric sine and cosine values using a combination of table lookup and linear interpolation. There are separate functions for Q31 and floating-point data types. The input to the floating-point version is in degrees while the fixed-point Q31 have a scaled input with the range [-1 0.9999] mapping to [-180 +180] degrees
PID Motor Control	A Proportional Integral Derivative (PID) controller is a generic feedback control loop mechanism widely used in industrial control systems. A PID controller is the most commonly used type of feedback controller
Vector Park Transform	Forward Park transform converts the input two-coordinate vector to flux and torque components. The Park transform can be used to realize the transformation of the Ialpha and the Ibeta currents from the stationary to the moving reference frame and control the spatial relationship between the stator vector current and rotor flux vector. If we consider the d axis aligned with the rotor flux, the diagram below shows the current vector and the relationship from the two reference frames:
Vector Inverse Park transform	Inverse Park transform converts the input flux and torque components to two-coordinate vector
Vector Clarke Transform	Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector. Generally the Clarke transform uses three-phase currents Ia, Ib and Ic to calculate currents in the two-phase orthogonal stator axis Ialpha and Ibeta. When Ialpha is superposed with Ia as shown in the figure below
Vector Inverse Clarke Transform	Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases
►Distance functions	Distance functions for use with clustering algorithms. There are distance functions for float vectors and boolean vectors
►Float Distances	Distances between two vectors of float values
Bray-Curtis distance	Bray-Curtis distance between two vectors
Canberra distance	Canberra distance
Chebyshev distance	Chebyshev distance
Cityblock (Manhattan) distance	Cityblock (Manhattan) distance
Correlation distance	Correlation distance
Cosine distance	Cosine distance
Dynamic Time Warping Distance	Dynamic Time Warping Distance
Euclidean distance	Euclidean distance
Jensen-Shannon distance	Jensen-Shannon distance
Minkowski distance	Minkowski distance
Boolean Distances	Distances between two vectors of boolean values
►Fast Math Functions	This set of functions provides a fast approximation to sine, cosine, and square root. As compared to most of the other functions in the NMSIS math library, the fast math functions operate on individual values and not arrays. There are separate functions for Q15, Q31, and floating-point data
ArcTan2	Computing Arc tangent only using the ratio y/x is not enough to determine the angle since there is an indeterminacy. Opposite quadrants are giving the same ratio
Cosine	Computes the trigonometric cosine function using a combination of table lookup and linear interpolation. There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians while the fixed-point Q15 and Q31 have a scaled input with the range [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a value of 2*pi wraps around to 0
Fixed point division
Sine	Computes the trigonometric sine function using a combination of table lookup and linear interpolation. There are separate functions for Q15, Q31, and floating-point data types. The input to the floating-point version is in radians while the fixed-point Q15 and Q31 have a scaled input with the range [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a value of 2*pi wraps around to 0
Vector Exponential	Compute the exp values of a vector of samples
Vector Log	Compute the log values of a vector of samples
Square Root	Computes the square root of a number. There are separate functions for Q15, Q31, and floating-point data types. The square root function is computed using the Newton-Raphson algorithm. This is an iterative algorithm of the form:
►Filtering Functions
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:
►Interpolation Functions	These functions perform 1- and 2-dimensional interpolation of data. Linear interpolation is used for 1-dimensional data and bilinear interpolation is used for 2-dimensional data
Bilinear Interpolation	Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid. The underlying function f(x, y) is sampled on a regular grid and the interpolation process determines values between the grid points. Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension. Bilinear interpolation is often used in image processing to rescale images. The NMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types
Linear Interpolation	Linear interpolation is a method of curve fitting using linear polynomials. Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
Cubic Spline Interpolation	Spline interpolation is a method of interpolation where the interpolant is a piecewise-defined polynomial called "spline"
►Matrix Functions	This set of functions provides basic matrix math operations. The functions operate on matrix data structures. For example, the type definition for the floating-point matrix structure is shown below:
Householder transform of a vector	Computes the Householder transform of a vector x
Matrix Addition	Adds two matrices
Cholesky and LDLT decompositions	Computes the Cholesky or LL^t decomposition of a matrix
Complex Matrix Multiplication	Complex Matrix multiplication is only defined if the number of columns of the first matrix equals the number of rows of the second matrix. Multiplying an M x N matrix with an N x P matrix results in an M x P matrix
Complex Matrix Transpose	Tranposes a complex matrix
Matrix Initialization	Initializes the underlying matrix data structure. The functions set the numRows, numCols, and pData fields of the matrix data structure
Matrix Inverse	Computes the inverse of a matrix
Matrix Multiplication	Multiplies two matrices
QR decomposition of a Matrix	Computes the QR decomposition of a matrix M using Householder algorithm
Matrix Scale	Multiplies a matrix by a scalar. This is accomplished by multiplying each element in the matrix by the scalar. For example:
Matrix Subtraction	Subtract two matrices
Matrix Transpose	Tranposes a matrix
Matrix Vector Multiplication	Multiplies a matrix and a vector
►Quaternion Math Functions	Functions to operates on quaternions and convert between a rotation and quaternion representation
►Quaternion conversions	Conversions between quaternion and rotation representations
Quaternion to Rotation	Conversions from quaternion to rotation
Rotation to Quaternion	Conversions from rotation to quaternion
Quaternion Conjugate	Compute the conjugate of a quaternion
Quaternion Inverse	Compute the inverse of a quaternion
Quaternion Norm	Compute the norm of a quaternion
Quaternion normalization	Compute a normalized quaternion
►Quaternion Product	Compute the product of quaternions
Elementwise Quaternion Product	Compute the elementwise product of quaternions
Quaternion Product	Compute the product of two quaternions
►Statistics Functions
Absolute Maximum	Computes the maximum value of absolute values of an array of data. The function returns both the maximum value and its position within the array. There are separate functions for floating-point, Q31, Q15, and Q7 data types
Absolute Minimum	Computes the minimum value of absolute values of an array of data. The function returns both the minimum value and its position within the array. There are separate functions for floating-point, Q31, Q15, and Q7 data types
Accumulation functions	Calculates the accumulation of the input vector. Sum is defined as the addition of the elements in the vector. The underlying algorithm is used:
Entropy	Computes the entropy of a distribution
Kullback-Leibler divergence	Computes the Kullback-Leibler divergence between two distributions
LogSumExp	LogSumExp optimizations to compute sum of probabilities with Gaussian distributions
Maximum	Computes the maximum value of an array of data. The function returns both the maximum value and its position within the array. There are separate functions for floating-point, Q31, Q15, and Q7 data types
Mean	Calculates the mean of the input vector. Mean is defined as the average of the elements in the vector. The underlying algorithm is used:
Minimum	Computes the minimum value of an array of data. The function returns both the minimum value and its position within the array. There are separate functions for floating-point, Q31, Q15, and Q7 data types
Mean Square Error	Calculates the mean square error between two vectors
Power	Calculates the sum of the squares of the elements in the input vector. The underlying algorithm is used:
Root mean square (RMS)	Calculates the Root Mean Square of the elements in the input vector. The underlying algorithm is used:
Standard deviation	Calculates the standard deviation of the elements in the input vector
Variance	Calculates the variance of the elements in the input vector. The underlying algorithm used is the direct method sometimes referred to as the two-pass method:
►Support Functions
Typecasting
Barycenter	Barycenter of weighted vectors
Vector sorting algorithms	Sort the elements of a vector
Vector Copy	Copies sample by sample from source vector to destination vector
Convert 16-bit floating point value
Convert 64-bit floating point value
Vector Fill	Fills the destination vector with a constant value
Convert 32-bit floating point value
Convert 16-bit fixed point value
Convert 32-bit fixed point value
Convert 8-bit fixed point value
Weighted Sum	Weighted sum of values
►SVM Functions	This set of functions is implementing SVM classification on 2 classes. The training must be done from scikit-learn. The parameters can be easily generated from the scikit-learn object. Some examples are given in DSP/Testing/PatternGeneration/SVM.py
Linear SVM	Linear SVM classifier
Polynomial SVM	Polynomial SVM classifier
RBF SVM	RBF SVM classifier
Sigmoid SVM	Sigmoid SVM classifier
►Transform Functions
►Complex FFT Functions
Complex FFT Tables
Complex FFT F16
Complex FFT F32
Complex FFT F64
Complex FFT Q15
Complex FFT Q31
Deprecated Complex FFT functions
►DCT Type IV Functions	Representation of signals by minimum number of values is important for storage and transmission. The possibility of large discontinuity between the beginning and end of a period of a signal in DFT can be avoided by extending the signal so that it is even-symmetric. Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the spectrum and is very widely used in signal and image coding applications. The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions. DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular
DCT Type IV Tables
DCT4 F32
DCT4 Q15
DCT4 Q31
►MFCC	MFCC Transform
MFCC F32
MFCC F16
MFCC Q15
MFCC Q31
►Real FFT Functions
Real FFT F16 Functions
Real FFT F64 Functions
Real FFT Q15 Functions
Real FFT Q31 Functions
Real FFT Tables
Real FFT F32 Functions
Deprecated Real FFT Functions
►Window Functions
►Flat-top window functions	Use those windows when you need to estimate the amplitude of a tone
Hft116d window function (116.8 dB)
Hft144d window function (144.1 dB)
Hft169d window function (169.5 dB)
Hft196d window function (196.2 dB)
Hft223d window function (223.0 dB)
Hft248d window function (248.4 dB)
Hft90d window function (90.2 dB)
Hft95 window function (95.0 dB)
►Regular window functions	Regular window functions that can be used for detecting tones or estimating the noise. If you need to estimate the amplitude of a tones, prefer a flat top window
Bartlett window function (26.5 dB)
Blackman Harris window function (92 dB)
Hamming window function (42.7 dB)
Hanning window function (31.5 dB)
Nuttall3 window function (46.7 dB)
Nuttall3a window function (64.2 dB)
Nuttall3b window function (71.5 dB)
Nuttall4 window function (60.9 dB)
Nuttall4a window function (82.6 dB)
Nuttall4b window function (93.3 dB)
Nuttall4c window function (98.1 dB)
Welch window function (21.3 dB)
►Examples
Bayes Example
Class Marks Example
Convolution Example
Dot Product Example
Frequency Bin Example
FIR Lowpass Filter Example
Graphic Audio Equalizer Example
Linear Interpolate Example	NMSIS DSP Software Library – Linear Interpolate Example
Matrix Example
Signal Convergence Example
SineCosine Example
SVM Example
Variance Example