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I have a scenario where ๐‘ฅ(๐‘ก)=2โ‹…sin150๐œ‹t +sin250๐œ‹t and g(t)=๐‘ฅ(๐‘ก)sin250๐œ‹ . The signal g(t) is passed as input through an ideal lowpass filter with cutoff frequency(fc)= 300๐œ‹ and passband gain= 3.

what will be the output signal of the lowpass filter? Please suggest if there is any formula or representation to calculate this?

I know the ideal function of a Low Pass filter is meant to block all high range frequencies and allow low frequencies. Can anyone suggest any formula to evaluate this?

I am new to this concept of filtering .

Kind regards

Sameer

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The ideal (and unrealizable) low pass filter is a brick-wall filter that will pass all frequencies below itโ€™s cutoff with a gain of 3 and reject everything above cutoff. The formula is simply a rectangular function and the exercise here for you is to see if you can recognize the individual frequencies and amplitudes in your formula for the waveform.

Use the sine product rule to determine g(t) and then see which of these frequency terms are above or below cutoff. For any frequency terms below cutoff, multiply the amplitude by the passband gain.

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  • $\begingroup$ First of all,Thankyou for your reply, could you please le me know what is the sine product rule, do you mean to say Fourier series?It will be great if you can show me with an example please based on my above scenario. $\endgroup$ Dec 14, 2021 at 12:05
  • $\begingroup$ @Powerbicloud Hi! We can't completely do your homework for you. You can easily find the sine product rule- your assignment here is quite simple actually so work through it based on the hints I provided, I am confident you will figure it out! Look for "Sine Product Formula" which is basically the formula for the product of $\sin(a)\sin(b)$ which is what you need to do here. $\endgroup$ Dec 14, 2021 at 12:07
  • $\begingroup$ thankyou for the response.Here is what I got after applying sine product formula g(t)=(2โ‹…sin150๐œ‹t +sin250๐œ‹t )sin250๐œ‹ g(t)= (cos(100๐œ‹t) - cos(400๐œ‹t ))+ 1/2(cos(0๐œ‹t )-cos(500๐œ‹t)) (because anything above 300 ๐œ‹ will be cut off) g(t)=cos(100๐œ‹t) +1/2(cos(0๐œ‹t ) ,could you please suggest if that looks ok and what about the pass band gain =3? where can we use that factor in the above equation $\endgroup$ Dec 15, 2021 at 2:49
  • $\begingroup$ Gain of 3 simply means it is 3 times larger $\endgroup$ Dec 15, 2021 at 5:37

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