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Fat32
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Forward DFT and Inverse DFT are quite similar transforms related by the following:

Let $x[n]$ be a length $N$ sequence, $X_f[k]$ be its N-point forward DFT, and $x_i[k]$ be its N-point inverse DFT : (ignore whatever that $k$ or $n$ refers to, let it be just a sequence index.)

$$X_f[k] = \text{DFT}\{x[n]\} = \sum_{n=0}^{N-1} x[n] e^{-j\frac{2\pi}{N}nk}$$ $$x_i[k] = \text{I-DFT}\{x[n]\} = \frac{1}{N}\sum_{n=0}^{N-1} x[n] e^{j\frac{2\pi}{N}nk}$$

Then $X_f[k]$ and $x_i[k]$ are related by:

$$ X_f[k] = N ~ x_i[-n] $$$$ X_f[k] = N ~ x_i[-k] $$

where $x_i[-n]$$x_i[-k]$ is the circularly reversed sequence $x_i[n]$$x_i[k]$.

As you can see, the forward and inverse DFT results are (almost) identical except a linear scale by $N$ and reversed ouput ordering. Hence, you can use either of them to compute the other, by performing the scaling and re-ordering properly.

Forward DFT and Inverse DFT are quite similar transforms related by the following:

Let $x[n]$ be a length $N$ sequence, $X_f[k]$ be its N-point forward DFT, and $x_i[k]$ be its N-point inverse DFT :

$$X_f[k] = \text{DFT}\{x[n]\} = \sum_{n=0}^{N-1} x[n] e^{-j\frac{2\pi}{N}nk}$$ $$x_i[k] = \text{I-DFT}\{x[n]\} = \frac{1}{N}\sum_{n=0}^{N-1} x[n] e^{j\frac{2\pi}{N}nk}$$

Then $X_f[k]$ and $x_i[k]$ are related by:

$$ X_f[k] = N ~ x_i[-n] $$

where $x_i[-n]$ is the circularly reversed sequence $x_i[n]$.

As you can see, the forward and inverse DFT results are (almost) identical except a linear scale by $N$ and reversed ouput ordering. Hence, you can use either of them to compute the other, by performing the scaling and re-ordering properly.

Forward DFT and Inverse DFT are quite similar transforms related by the following:

Let $x[n]$ be a length $N$ sequence, $X_f[k]$ be its N-point forward DFT, and $x_i[k]$ be its N-point inverse DFT : (ignore whatever that $k$ or $n$ refers to, let it be just a sequence index.)

$$X_f[k] = \text{DFT}\{x[n]\} = \sum_{n=0}^{N-1} x[n] e^{-j\frac{2\pi}{N}nk}$$ $$x_i[k] = \text{I-DFT}\{x[n]\} = \frac{1}{N}\sum_{n=0}^{N-1} x[n] e^{j\frac{2\pi}{N}nk}$$

Then $X_f[k]$ and $x_i[k]$ are related by:

$$ X_f[k] = N ~ x_i[-k] $$

where $x_i[-k]$ is the circularly reversed sequence $x_i[k]$.

As you can see, the forward and inverse DFT results are (almost) identical except a linear scale by $N$ and reversed ouput ordering. Hence, you can use either of them to compute the other, by performing the scaling and re-ordering properly.

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Fat32
  • 28.4k
  • 3
  • 24
  • 51

Forward DFT and Inverse DFT are quite similar transforms related by the following:

Let $x[n]$ be a length $N$ sequence, $X_f[k]$ be its N-point forward DFT, and $x_i[k]$ be its N-point inverse DFT :

$$X_f[k] = \text{DFT}\{x[n]\} = \sum_{n=0}^{N-1} x[n] e^{-j\frac{2\pi}{N}nk}$$ $$x_i[k] = \text{I-DFT}\{x[n]\} = \frac{1}{N}\sum_{n=0}^{N-1} x[n] e^{j\frac{2\pi}{N}nk}$$

Then $X_f[k]$ and $x_i[k]$ are related by:

$$ X_f[k] = N ~ x_i[-n] $$

where $x_i[-n]$ is the circularly reversed sequence $x_i[n]$.

As you can see, the forward and inverse DFT results are (almost) identical except a linear scale by $N$ and reversed ouput ordering. Hence, you can use either of them to compute the other, by performing the scaling and re-ordering properly.