cfir1d(3S)
CFIR1D, ZFIR1D, SFIR1D, DFIR1D - Compute the 1D convolution of a sequence
As shipped in IRIX 6.5.15. Added in IRIX 6.5.15.
NAME CFIR1D, ZFIR1D, SFIR1D, DFIR1D - Compute the 1D convolution of a sequence SYNOPSIS Single precision complex Fortran: CALL CFIR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0, ny, alpha, beta) C/C++: #include <scsl_fft.h> void cfir1d( scsl_complex *x, int incx, int ix0, int nx, scsl_complex *h, int inch, int ih0, int nh, scsl_complex *y, int incy, int iy0, int ny, scsl_complex *alpha, scsl_complex *beta); C++ STL: #include <complex.h> #include <scsl_fft.h> void cfir1d( complex<float> *x, int incx, int ix0, int nx, complex<float> *h, int inch, int ih0, int nh, complex<float> *y, int incy, int iy0, int ny, complex<float> *alpha, complex<float> *beta); Double precision complex Fortran: CALL ZFIR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0, ny, alpha, beta) C/C++: #include <scsl_fft.h> void zfir1d( scsl_zomplex *x, int incx, int ix0, int nx, scsl_zomplex *h, int inch, int ih0, int nh, scsl_zomplex *y, int incy, int iy0, int ny, scsl_zomplex *alpha, scsl_zomplex *beta); C++ STL: #include <complex.h> #include <scsl_fft.h> void zfir1d( complex<double> *x, int incx, int ix0, int nx, complex<double> *h, int inch, int ih0, int nh, complex<double> *y, int incy, int iy0, int ny, complex<double> *alpha, complex<double> *beta); Single precision Fortran: CALL SFIR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0, ny, alpha, beta) C/C++: #include <scsl_fft.h> void sfir1d( float *x, int incx, int ix0, int nx, float *h, int inch, int ih0, int nh, float *y, int incy, int iy0, int ny, float alpha, float beta); Double precision Fortran: CALL DFIR1D (x, incx, ix0, nx, h, inch, ih0, nh, y, incy, iy0, ny, alpha, beta) C/C++: #include <scsl_fft.h> void dfir1d( double *x, int incx, int ix0, int nx, double *h, int inch, int ih0, int nh, double *y, int incy, int iy0, int ny, double alpha, double beta); IMPLEMENTATION These routines are part of the SCSL Scientific Library and can be loaded using either the -lscs or the -lscs_mp option. The -lscs_mp option directs the linker to use the multi-processor version of the library. When linking to SCSL with -lscs or -lscs_mp, the default integer size is 4 bytes (32 bits). Another version of SCSL is available in which integers are 8 bytes (64 bits). This version allows the user access to larger memory sizes and helps when porting legacy Cray codes. It can be loaded by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use only one of the two versions; 4-byte integer and 8-byte integer library calls cannot be mixed. The C and C++ prototypes shown above are appropriate for the 4-byte integer version of SCSL. When using the 8-byte integer version, the variables of type int become long long and the <scsl_fft_i8.h> header file should be included. DESCRIPTION These routines compute the convolution of the finite impulse response filter h with a vector x, producing the output vector y. y = beta * y + alpha * h * x Suppose h and x are two sequences of numbers having nh and nx elements respectively: h = [h(0), h(1), , h(nh - 1) ] , and x = [x(0), x(1), , x(nx - 1) ] . The convolution product, y = h*x, is the sequence that has nh + nx - 1 non-zero elements defined by the following: nh-1 y(j) = Sum [h(k)x(j-k)] for j=0, ...,nx+nh-2 j=0 y(0) = h(0)*x(0) y(1) = h(0)*x(1) + h(1)*x(0) y(2) = h(0)*x(2) + h(1)*x(1) + h(2)*x(0) y(nh-1) = h(0)*x(nh-1) + h(1)*x(nh-2) + ... + h(nh-1)*x(0) ... y(j) = h(0)*x(j) + h(1)*x(j-1) + ... + h(nh-1)*x(j-nh+1) ... y(nx-1) = h(0)*x(nx-1) + h(1)*x(nx-2) + ... + h(nh-1)*x(nx-nh) ... y(nx+nh-3) = h(nh-2)*x(nx-1) + h(nh-1)*x(nx-2) y(nx+nh-2) = h(nh-1)*x(nx-1) In the *FIR1D routines, the number of terms in the output sequence is specified by an argument, ny. If ny < nh + nx - 1 the sequence y is truncated. If ny > nh + nx - 1 the terms beyond y(nh + nx - 2) are set to 0. Generally, the sequences x, h and y represent signals sampled at equal time intervals, and the indexes of the vectors denote the sample times. If all three signals begin at the same time, we may, without loss of generality, set the initial time to 0, as in the formulas above. The *FIR1D routines, however, permit more generality than this. The signals may be time shifted from each other using input parameters specifiying the initial time sample for each signal. This can be useful in several situations. For example, if the input array has several leading zero values that one does not wish to store, ix0 may be set to the time sample corresponding to the first non-zero element in the input array, and earlier time samples are treated as 0. Another use is to limit the output to just the "fully engaged" terms of the convolution. As can be seen above, when nx>= nh, the convolution has ramp-up and ramp-down regions in which fewer than all nh filter values contribute to the output value. Setting iy0 to nh-1 causes the first value output to correspond to time sample nh-1, thus skipping the ramp-up region. Setting ny to nx-nh+1 then drops the ramp-down terms, limiting the output to just the fully engaged part. Note that, instead of 0, the initial time could just as easily have been labeled 1 or 10 or -78; the relevant point is that the first elements of each of the x, h and y arrays are defined to be the same time sample as long as ix0 = ih0 = iy0. See the NOTES section of this man page for information about the interpretation of the data types described in the following arguments. These routines have the following arguments: x Array of dimension nx. (input). CFIR1D: Single precision complex array. ZFIR1D: Double precision complex array. SFIR1D: Single precision array. DFIR1D: Double precision array. Input sequences to be convolved with h. incx Integer. (input) The increment between two successive values of x. incx must not be 0. ix0 Integer. (input) Time sample corresponding to the first element of x. nx Integer. (input) The number of elements in the sequence x. nx >= 0. h Array of dimension nh. (input). CFIR1D: Single precision complex array. ZFIR1D: Double precision complex array. SFIR1D: Single precision array. DFIR1D: Double precision array. Input sequence to be convolved with x. inch Integer. (input) Increment between two successive values of h. inch must not be 0. ih0 Integer. (input) Time sample corresponding to the first element of h. nh Integer. (input) The number of elements in the sequence h. nh >= 0. y Array of dimension ny. (input and output). CFIR1D: Single precision complex array. ZFIR1D: Double precision complex array. SFIR1D: Single precision array. DFIR1D: Double precision array. Output of the FIR filter. On entry, the array y must have been initialized, except except when beta is 0; in that case, y need not be initialized. On exit, the result overwrites y. incy Integer. (input) Increment between two successive values of y. incy must not be 0. iy0 Integer. (input) Time sample corresponding to the first element of y. ny Integer. (input) Number of elements in the sequence y. ny >= 0. alpha Scale factor for the convolution. (input). CFIR1D: Single precision complex. ZFIR1D: Double precision complex. SFIR1D: Single precision. DFIR1D: Double precision. For C/C++, a pointer to this value is passed. beta Scale factor for the output y. (input) CFIR1D: Single precision complex. ZFIR1D: Double precision complex. SFIR1D: Single precision. DFIR1D: Double precision. When beta is supplied as 0, y need not be set on input. For C/C++, a pointer to this value is passed. NOTES The following data types are described in this documentation: Term Used Data type Fortran: Array dimensioned 0..n-1 x(0:n-1) Array of dimensions (m,n) x(m,n) Array of dimensions (m,n,p) x(m,n,p) Integer INTEGER (INTEGER*8 for -lscs_i8[_mp]) Single precision REAL Double precision DOUBLE PRECISION Single precision complex COMPLEX Double precision complex DOUBLE COMPLEX C/C++: Array dimensioned 0..n-1 x[n] Array of dimensions (m,n) x[m*n] or x[n][m] Array of dimensions (m,n,p) x[m*n*p] or x[p][n][m] Integer int (long long for -lscs_i8[_mp]) Single precision float Double precision double Single precision complex scsl_complex Double precision complex scsl_zomplex C++ STL: Array dimensioned 0..n-1 x[n] Array of dimensions (m,n) x[m*n] or x[n][m] Array of dimensions (m,n,p) x[m*n*p] or x[p][n][m] Integer int (long long for -lscs_i8[_mp]) Single precision float Double precision double Single precision complex complex<float> Double precision complex complex<double> CAUTIONS The arrays x, h, and y must be non-overlapping. EXAMPLES The following example computes the convolution of a 4-sample sequence x with a filter h containing 3 samples. Fortran: REAL X(0:3), H(0:2), Y(0:5) REAL ALPHA, BETA ALPHA = 1.0 BETA = 0.0 X(0) = 1.0 DO I = 1, 3 X(I) = -1.0 ENDDO DO I = 0, 2 H(I) = 1.0/(I+1) ENDDO CALL SFIR1D(X(0), 1, 0, 4, H(0), 1, 0, 3, Y(0), 1, 0, 6, & ALPHA, BETA) C/C++: #include <scsl_fft.h> float x[4], h[3], y[6]; float alpha = 1.0f; float beta = 0.0f; int i; x[0] = 1.0f for (i=1; i<4; i++) { x[i] = -1.0f; } for (i=0; i<3; i++) { h[i] = 1.0f/(i+1); } sfir1d(x, 1, 0, 4, h, 1, 0, 3, y, 1, 0, 6, alpha, beta); The output is the following: Y(0) Y(1) Y(2) Y(3) Y(4) Y(5) 1.0000 -0.5000 -1.1667 -1.8333 -0.8333 -0.3333 Changing the values for ix0, ih0 and iy0 produces the following shifts in the output: Y(0) Y(1) Y(2) Y(3) Y(4) Y(5) ix0 = +1: 0.0000 1.0000 -0.5000 -1.1667 -1.8333 -0.8333 ix0 = +2: 0.0000 0.0000 1.0000 -0.5000 -1.1667 -1.8333 ix0 = -1: -0.5000 -1.1667 -1.8333 -0.8333 -0.3333 0.0000 ix0 = -2: -1.1667 -1.8333 -0.8333 -0.3333 0.0000 0.0000 ih0 = +1: 0.0000 1.0000 -0.5000 -1.1667 -1.8333 -0.8333 ih0 = +2: 0.0000 0.0000 1.0000 -0.5000 -1.1667 -1.8333 ih0 = -1: -0.5000 -1.1667 -1.8333 -0.8333 -0.3333 0.0000 ih0 = -2: -1.1667 -1.8333 -0.8333 -0.3333 0.0000 0.0000 iy0 = +1: -0.5000 -1.1667 -1.8333 -0.8333 -0.3333 0.0000 iy0 = +2: -1.1667 -1.8333 -0.8333 -0.3333 0.0000 0.0000 iy0 = -1: 0.0000 1.0000 -0.5000 -1.1667 -1.8333 -0.8333 iy0 = -2: 0.0000 0.0000 1.0000 -0.5000 -1.1667 -1.8333 SEE ALSO INTRO_FFT(3S), INTRO_SCSL(3S)