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This is the shape of the bipolar amplitude function for a FIR filter with odd m:

enter image description here

I have 2 questions :

  1. If i want to use this FIR as a low pass filter between 0 and $\frac{F_{c}}{2}$ , how can i set the value of $G(f)$ to 0 between $\frac{F_{c}}{2}$ and $F_{c}$ ?

  2. My prof said that i can use the this FIR as a lowpass between 0 and $\frac{F_{c}}{2}$, but if i want to use the filter between $\frac{F_{c}}{2}$ and $F_{c}$ does it still behave as a lowpass ? (what does it mean that in that range $G(f)$ takes negative values ? )

Marcus Müller
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themagiciant95
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  • this isn't even a low pass between 0 and $F_c/2$, even if it was a good idea to zero-force the rest, so I'm not even sure where this is coming from or going to. – Marcus Müller Jan 14 '20 at 08:54
  • also, a how did you determine this $G(f)$? this doesn't look like it was done with the tools you could apply to a discrete-time system like your FIR filter probably is. – Marcus Müller Jan 14 '20 at 08:56
  • It's on a slide did by my prof. You can watch it here https://ibb.co/4FYxvVL – themagiciant95 Jan 14 '20 at 10:10
  • The figure on the slide looks different from the one in your question. – Matt L. Jan 14 '20 at 10:15
  • I'm sorry wrong slide, https://ibb.co/YjjdW3T – themagiciant95 Jan 14 '20 at 10:23
  • @themagiciant95 ok, but your $G(f)$ still isn't a low-pass filter. The $\tilde H(f)$ from that slide can be one, given appropriate frequency-shifting through the complex exponential. Again, you usually don't "zero out" something in the discrete Fourier domain (see this). – Marcus Müller Jan 14 '20 at 12:09
  • Thanks for the help, i heard clearly my prof saying that i can use that filter as a low pass filter in the first half of the diagram. In your opinion, what did he mean? – themagiciant95 Jan 14 '20 at 12:15
  • This is a low pass filter if $F_c$ is the sampling rate; I think that may be some source of confusion – Dan Boschen Jan 14 '20 at 17:00
  • Hi, thanks. Could you answer with more details to my initial question ? – themagiciant95 Jan 14 '20 at 17:09
  • Yes I can help point you in the right direction - to answer this you need to understand better what the spectrum looks like for a digital sampled signal and what the concept of negative frequency is. Do you see that if I sample a signal at $F_c$ that the unique frequency spectrum extends from $-\F_c/2$ to $+\F_c/2$? – Dan Boschen Jan 15 '20 at 15:01

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