sp.firwin
=========

.. automodule:: sp.firwin

Example Usage
^^^^^^^^^^^^^

Building a Lowpass Filter
_________________________

::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #Low pass
    M = 100 #number of taps in filter
    fc = 0.25 #i.e. normalised cutoff frequency 1/4 of sampling rate i.e. 25Hz
    lp = firwin.build_filter(M, fc, window=firwin.blackman)

    #filter the signal
    filtered = numpy.convolve(signal, lp)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(lp)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

.. plot::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #Low pass
    M = 100 #number of taps in filter
    fc = 0.25 #i.e. normalised cutoff frequency 1/4 of sampling rate i.e. 25Hz
    lp = firwin.build_filter(M, fc, window=firwin.blackman)

    #filter the signal
    filtered = numpy.convolve(signal, lp)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(lp)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

Building a Highpass Filter
__________________________

::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #First build a Lowpass filter
    M = 100 #number of taps in filter
    fc = 0.25 #i.e. normalised cutoff frequency 1/4 of sampling rate i.e. 25Hz
    lp = firwin.build_filter(M, fc, window=firwin.blackman)
    #next build Highpass filter by shifting frequency domain
    shift = numpy.cos(2*numpy.pi*0.5*numpy.arange(M + 1))
    hp = lp*shift

    #filter the signal
    filtered = numpy.convolve(signal, hp)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(hp)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

.. plot::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #First build a Lowpass filter
    M = 100 #number of taps in filter
    fc = 0.25 #i.e. normalised cutoff frequency 1/4 of sampling rate i.e. 25Hz
    lp = firwin.build_filter(M, fc, window=firwin.blackman)
    #next build Highpass filter by shifting frequency domain
    shift = numpy.cos(2*numpy.pi*0.5*numpy.arange(M + 1))
    hp = lp*shift

    #filter the signal
    filtered = numpy.convolve(signal, hp)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(hp)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

Building a Bandpass Filter
__________________________

::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #first need a low-pass with fc 0.35
    M = 100 #number of taps in filter
    fc = 0.35
    lp = firwin.build_filter(M, fc, window=firwin.blackman)
    shift = numpy.cos(2*numpy.pi*0.5*numpy.arange(M + 1))
    hp = lp*shift
    #now we can create the bandpass filter by convolution
    bp = numpy.convolve(lp, hp)

    #filter the signal
    filtered = numpy.convolve(signal, bp)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(bp)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

.. plot::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #first need a low-pass with fc 0.35
    M = 100 #number of taps in filter
    fc = 0.35
    lp = firwin.build_filter(M, fc, window=firwin.blackman)
    shift = numpy.cos(2*numpy.pi*0.5*numpy.arange(M + 1))
    hp = lp*shift
    #now we can create the bandpass filter by convolution
    bp = numpy.convolve(lp, hp)

    #filter the signal
    filtered = numpy.convolve(signal, bp)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(bp)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

Building a Bandstop Filter
__________________________

::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #first need a low-pass with fc 0.15
    M = 100 #number of taps in filter
    fc = 0.15
    lp = firwin.build_filter(M, fc, window=firwin.blackman)
    #next need a high-pass
    shift = numpy.cos(2*numpy.pi*0.5*numpy.arange(M + 1))
    hp = lp*shift
    #now we can create the bandstop filter by adding the two impulse responses
    bs = lp + hp

    #filter the signal
    filtered = numpy.convolve(signal, bs)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(bs)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

.. plot::

    import numpy
    import pylab

    from sp import firwin

    f0 = 20 #20Hz
    ts = 0.01 # i.e. sampling frequency is 1/ts = 100Hz
    x = numpy.arange(-10, 10, ts)
    signal = (numpy.cos(2*numpy.pi*f0*x) + numpy.sin(2*numpy.pi*2*f0*x) + 
                numpy.cos(2*numpy.pi*0.5*f0*x) + numpy.cos(2*numpy.pi*1.5*f0*x))

    #build filter
    #first need a low-pass with fc 0.15
    M = 100 #number of taps in filter
    fc = 0.15
    lp = firwin.build_filter(M, fc, window=firwin.blackman)
    #next need a high-pass
    shift = numpy.cos(2*numpy.pi*0.5*numpy.arange(M + 1))
    hp = lp*shift
    #now we can create the bandstop filter by adding the two impulse responses
    bs = lp + hp

    #filter the signal
    filtered = numpy.convolve(signal, bs)

    #plotting
    pylab.figure()
    pylab.subplot(3,1,1)
    pylab.title('Original Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(signal)
    pylab.subplot(3,1,2)
    pylab.title('Filter Frequency Response')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(bs)
    #window and fft
    pylab.subplot(3,1,3)
    pylab.title('Filtered Spectrum')
    pylab.xlabel('Normalised Frequency')
    firwin.plot_fft(firwin.hamming(len(filtered))[:-1]*(filtered))
    pylab.subplots_adjust(hspace = 0.6)
    pylab.show()

See the individual methods below for further details.

Functions
^^^^^^^^^

.. autofunction:: sp.firwin.blackman

.. autofunction:: sp.firwin.build_filter

.. autofunction:: sp.firwin.hamming

.. autofunction:: sp.firwin.plot_fft

.. autofunction:: sp.firwin.sinc_filter