DSB-SC Double Sideband Supressed Carrier
Define rect().
Choose
cycles of the modulation
frequency.
This is the modulating signal, m(t).
We use Π() to limit the time duration of the signal.
The fourier transform of this truncated funtion will then
not have any "infinitely high" delta functions.
We cannot integrate a sinusoid from minus infinity to infinity.
Here is our DSB-SC signal.
Estimate the time range, tmax,
multiple of one over the filter bandwidth.
Next, find the Fourier transform of the signal.
In some cases, the
Note: Fourier integral may not evaluate properly with infinite limits, so evaluate over limits that reasonably encompass the nonzero region of the function
Estimate the frequency range, fmax,
mm(t) is defined as A+m(t)
Define m(t).
Then, use the convolution form of the Hilbert transform.
Split the integral to avoid
the problems with
infinite value of 1/(t-
First, define m(t) and set the sampling parameters
If we use the integral above, we will slow down our computations below.
Since we know that the hilbert transform should give a 90 degree phase shift,
we approximate it directly as:
Finally, create the SSB signal:
Create lower sideband modulated signal.
Find the frequency spectrum :