Skip to main content
Mathematics

Return to Question

added 37 characters in body
Source Link
JMoser
JMoser
  • 31
  • 5

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that $|a| < 1$ and , $\Omega_0 < \pi$, and u[n] being the unit step function.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] \iff X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that $|a| < 1$ and $\Omega_0 < \pi$.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] \iff X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that $|a| < 1$, $\Omega_0 < \pi$, and u[n] being the unit step function.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] \iff X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

added 2 characters in body; edited title
Source Link
user147263
user147263

DTFT Discrete Time Fourier Transform of athe signal, not sure where to start represented by $x[n] = n^2 a^n u[n]$

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that |a| < 1$|a| < 1$ and $\Omega_0 < \pi$.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] <==> X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$$$ x[n] = a^nu[n] \iff X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

DTFT of a signal, not sure where to start

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that |a| < 1 and $\Omega_0 < \pi$.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] <==> X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

Discrete Time Fourier Transform of the signal represented by $x[n] = n^2 a^n u[n]$

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that $|a| < 1$ and $\Omega_0 < \pi$.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] \iff X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.

Source Link
JMoser
JMoser
  • 31
  • 5

DTFT of a signal, not sure where to start

I have a homework problem that I am just not sure where to start with. I have to take the Discrete Time Fourier Transform of a signal represented by:

$$x[n] = n^2 a^n u[n]$$

given that |a| < 1 and $\Omega_0 < \pi$.

There is a hint saying that "Calculus and derivatives will help!" but that actually confuses me more than it helps. However, regardless, I'm just not sure how to even get started evaluating that. I know how to take the DTFT of a signal, but just can't figure out how to get it into a usable form. I also am allowed to use the following conversion:

$$ x[n] = a^nu[n] <==> X(\Omega) = \frac{e^{j\Omega}}{e^{j\Omega} - a}$$

I am not looking for the answer, but rather just some pointers as to how to start manipulating the original signal.