414 Seismograms as Signals
C-5. (a) Write a subroutine, using the results of C-2 and C-4, to use
the fast Fourier transform to convolve two time series.
(b) Use it on two boxcar functions of unit amplitude, one 6 s long
and one 3 s long.
C-6. (a) Write a subroutine to do time domain convolution of two
functions of different lengths, both sampled at a time step ∆t.
(b) Use it on two boxcar functions of unit amplitude, one 6 s long
and one 3 s long. Compare the results to those of C-5b.
C-4. (a) Write a subroutine, using the results of C-2, to use the fast
Fourier transform to take a time series, filter it in the frequency domain over a specified passband, and invert the FFT,
yielding a filtered time series. The subroutine should have the
capability to taper in the frequency domain. This subroutine
is best written as a set of subroutines.
(b) Use this routine to filter the time series in C-3e to isolate the
two different frequency components.
C-5. (a) Write a subroutine, using the results of C-2 and C-4, to use
the fast Fourier transform to convolve two time series.
(b) Use it on two boxcar functions of unit amplitude, one 6 s long
and one 3 s long.
C-6. (a) Write a subroutine to do time domain convolution of two
functions of different lengths, both sampled at a time step ∆t.
(b) Use it on two boxcar functions of unit amplitude, one 6 s long
and one 3 s long. Compare the results to those of C-5b.
C-4. (a) Write a subroutine, using the results of C-2, to use the fast
Fourier transform to take a time series, filter it in the frequency domain over a specified passband, and invert the FFT,
yielding a filtered time series. The subroutine should have the
capability to taper in the frequency domain. This subroutine
is best written as a set of subroutines.
(b) Use this routine to filter the time series in C-3e to isolate the
two different frequency components.