The DTFT is investigated in this project
Define rect(),rectangular pulse.
Create a sinc-squared pulse signal x(t)
This is the continuous-time signal, x(t).
We use rect() to limit the time duration of the signal, since cannot integrate from minus infinity to infinity.The Fourier transform of this truncated funtion will then not be exactly the same as for the infinite length function .
Next, find the Fourier transform of the signal.
In some cases, the
sin/cos form
Hint: the fourier transform pair is
<=>
Since it is not possible to simulate the impulse train
it will be approximated with unit-area rectangular pulses of width 0.05 and height 20,
with period Ts.
The sampled signal xs(t) is approximated as:
The spectrum of the sampled signal is
which can be approximated by:
which, for faster computation in Mathcad, can be approximated by
In mathcad notation, subscripts are used to indicate arrays of data,
so below we will let discrete-time signal x[n] be denoted as xx with a subscript n
first, set the number of samples,
For the sampling period Ts, the discrete-time version of x(t) is then
Since x[n] is zero outside the range of 0 to maxn,
the DTFT ( discrete-time Fourier transform)