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komm.TransmitFilter

Transmit filter (pulse shaping). Given a sequence of $N$ real or complex symbols $x[n]$, this filter outputs samples of the signal $$ x(t) = \sum_{n=0}^{N-1} x[n] h(t - n), $$ where $h(t)$ is the waveform of a given pulse, and the samples of the output signal are taken at an integer rate of $\beta$ samples per symbol. Note that the symbol interval is normalized to $1$.

The time span of $x(t)$ is given by $[ n_0, n_1 + N - 1 )$, where $[ n_0, n_1 )$ is the integer-bounded time span of $h(t)$. In turn, $n_0$ and $n_1$ depend on the support of $h(t)$:

  • If $h(t)$ has finite support $[ t_0, t_1 ]$, then $n_0 = \lfloor t_0 \rfloor$ and $n_1 = \lceil t_1 \rceil$.

  • If $h(t)$ has infinite support, then $n_0 = -L/2$ and $n_1 = L/2$, where $L$ is a given even positive integer, called the truncation window length.

Attributes:

  • pulse (Pulse) –

    The pulse whose waveform is $h(t)$.

  • samples_per_symbol (int) –

    The number $\beta$ of samples (of the output) per symbol (of the input). Must be a positive integer.

  • truncation (Optional[int]) –

    The truncation window length $L$. Only applies to infinite-duration pulses. Must be an even positive integer. The default value is 32.

Input:

  • symbols (Array1D[float] | Array1D[complex]) –

    The input symbols $x[n]$, of length $N$.

Output:

  • signal (SameAsInput) –

    The samples of the output signal $x(t)$, of length $(N + n_1 - n_0 - 1) \beta$.

Examples:

>>> pulse = komm.RectangularPulse(width=1.0)
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=3)
>>> tx_filter([1.0, -1.0, 1.0, 1.0])
array([ 1.,  1.,  1., -1., -1., -1.,  1.,  1.,  1.,  1.,  1.,  1.])

>>> pulse = komm.RectangularPulse(width=0.25)
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=3)
>>> tx_filter([1.0, -1.0, 1.0, 1.0])
array([ 1.,  0.,  0., -1.,  0.,  0.,  1.,  0.,  0.,  1.,  0.,  0.])

>>> pulse = komm.SincPulse()
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=4, truncation=4)
>>> tx_filter([1.0, -1.0, 1.0, 1.0]).reshape((-1, 4)).round(6)
array([[-0.      , -0.128617, -0.212207, -0.180063],
       [ 0.      ,  0.428722,  0.848826,  1.08038 ],
       [ 1.      ,  0.471594, -0.212207, -0.780274],
       [-1.      , -0.908891, -0.424413,  0.291531],
       [ 1.      ,  1.380485,  1.485446,  1.329038],
       [ 1.      ,  0.720253,  0.424413,  0.171489],
       [ 0.      , -0.180063, -0.212207, -0.128617]])

>>> pulse = komm.RectangularPulse()
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=4, truncation=4)
Traceback (most recent call last):
...
ValueError: parameter 'truncation' is only applicable to pulses with infinite support

pulse_time_span: tuple[int, int] cached property

The integer-bounded time span $[ n_0, n_1 )$ of the pulse waveform $h(t)$.

Examples:

>>> pulse = komm.RectangularPulse(0.25)
>>> pulse.support
(0.0, 0.25)
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=3)
>>> tx_filter.pulse_time_span
(0, 1)

>>> pulse = komm.SincPulse()
>>> pulse.support
(-inf, inf)
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=4, truncation=4)
>>> tx_filter.pulse_time_span
(-2, 2)

taps: npt.NDArray[np.float64] cached property

The FIR filter taps of the transmit filter.

Examples:

>>> pulse = komm.RectangularPulse(width=0.25)
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=3)
>>> tx_filter.taps
array([1., 0., 0.])

>>> pulse = komm.SincPulse()
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=4, truncation=4)
>>> tx_filter.taps.reshape((-1, 4)).round(6)
array([[-0.      , -0.128617, -0.212207, -0.180063],
       [ 0.      ,  0.300105,  0.63662 ,  0.900316],
       [ 1.      ,  0.900316,  0.63662 ,  0.300105],
       [ 0.      , -0.180063, -0.212207, -0.128617]])

time

Convenience function to generate the time axis of the output signal given the input symbols.

Parameters:

  • symbols (Array1D[float] | Array1D[complex]) –

    The input symbols $x[n]$, of length $N$.

Returns:

  • t (Array1D[float]) –

    The time axis of the output signal, of length $(N + n_1 - n_0 - 1) \beta$.

Examples:

>>> pulse = komm.RectangularPulse()
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=3)
>>> tx_filter.time([1.0, -1.0, 1.0, 1.0]).round(2)
array([0.  , 0.33, 0.67, 1.  , 1.33, 1.67, 2.  , 2.33, 2.67, 3.  , 3.33, 3.67])

>>> pulse = komm.SincPulse()
>>> tx_filter = komm.TransmitFilter(pulse=pulse, samples_per_symbol=4, truncation=4)
>>> tx_filter.time([1.0, -1.0, 1.0, 1.0]).reshape((-1, 4))
array([[-2.  , -1.75, -1.5 , -1.25],
       [-1.  , -0.75, -0.5 , -0.25],
       [ 0.  ,  0.25,  0.5 ,  0.75],
       [ 1.  ,  1.25,  1.5 ,  1.75],
       [ 2.  ,  2.25,  2.5 ,  2.75],
       [ 3.  ,  3.25,  3.5 ,  3.75],
       [ 4.  ,  4.25,  4.5 ,  4.75]])