Spectrum representation of signal in Low Pass Range

[sameer7]

Hi All,

I am new to DSP and with the little knowledge I have earned, I was trying to solve a problem as below.
A signal 𝑥𝐿(𝑡)= 𝑗𝑋0 sinc(𝐵 ) is in the lowpass range. what will be the formula representation of the bandpass signal 𝑥(𝑡)
if the transformation is performed respect to the cutoff frequency 𝑓𝑐=5𝐵? What is the spectrum 𝑋(𝑓) of 𝑥(𝑡) ( try only formula representation)?

Could anyone suggest the formula representation based on the above scenario. Also,Please take into consideration the cutoff frequency.

As per my approach and understanding, the signal should look as below :-
xL(t) = (jX0 sinc(Bt))e^j2πfct
xL(t) = (jX0 sinc(Bt))e^j10πBt (because In the time domain the above operation is done by simply multiplying the
the complex baseband signal by ej2πfct)

Please suggest your thoughts.

Sincerely,
Sameer

 

[BradtheRad]

The rolloff curve is described in terms of decibels per octave, or decibels per decade. It depends on the order number of the filter.

There's a relationship between phase change and attenuation of a frequency.

* For a low pass filter there is a frequency bound at the slower side where the filter has slight attenuating effect.

* At the cutoff frequency attenuating effect is noticeable (3 dB for one capacitor or one inductor).

* With increased frequency the attenuation is greater.

* There is a frequency bound at the faster side where the incoming signal becomes attenuated to an extent that it practically disappears.