MHB What Is the Relation Between \( x(n) \) and \( X(f) \) Given \( f = kn \)?

[maysam1]

Suppose that there is a linear relation between discrete time (n) and frequency (f), then what is the relatian between x(n) and X(f) (X(f) is DFT transform of x(n))?

 

[I like Serena]

Suppose that there is a linear relation between discrete time (n) and frequency (f), then what is the relatian between x(n) and X(f) (X(f) is DFT transform of x(n))?

Hi maysam! Welcome to MHB! (Smile)

I guess we'll need to find the DFT transform of $x(n)=c\cdot n$ where $c$ is some constant.
Can you calculate it?
What is the formula for a DFT?

 

[maysam1]

Hi maysam! Welcome to MHB! (Smile)

I guess we'll need to find the DFT transform of $x(n)=c\cdot n$ where $c$ is some constant.
Can you calculate it?
What is the formula for a DFT?

Hi, x(n) can be any signal.

 

[I like Serena]

Hi, x(n) can be any signal.

Hmm... can you clarify what a "linear relation between discrete time (n) and frequency (f)" means?

Presumably we have a signal amplitude $x(n) = x(t_n)$ that depends on time, which transforms to a signal amplitude $X(f) = X(f_k)$ that depends on frequency.
There is no relation between time and frequency.

 

[maysam1]

Hmm... can you clarify what a "linear relation between discrete time (n) and frequency (f)" means?

Presumably we have a signal amplitude $x(n) = x(t_n)$ that depends on time, which transforms to a signal amplitude $X(f) = X(f_k)$ that depends on frequency.
There is no relation between time and frequency.

Yes, originally There is no relation between time and frequency but In a system we can assume that f=kn and k is a constant. this means that in this system we can see a linear relation between time and frequency.