NDK_IDFT

Calculates the inverse discrete fast Fourier transformation, recovering the time series.

Return Value

a value from NDK_RETCODE enumeration for the status of the call. 

NDK_SUCCESS	operation successful
Error	Error Code

Parameters

[in]	amp	is an array of the amplitudes of the fourier transformation components.
[in]	phase	is an array of the phase angle (radian) of the Fourier transformation components .
[in]	nSize	is the number of spectrum components (i.e. size of amp and phase).
[out]	data	is the filtered (recovered) time series output
[in]	nSize	is the original number of observations used to calculate the fourier transform.

Remarks

1. The input time series may include missing values (NaN) at either end, but they will not be included in the calculations.
2. The input time series must be homogeneous or equally spaced.
3. The first value in the input time series must correspond to the earliest observation.
4. The frequency component order, \(k\), must be a positive number less than \(N\), or an error (#VALUE!) is returned.
5. The DFT returns the phase angle in radians; i.e. \( 0 \lt \phi \lt 2 \times \pi\).
6. The discrete Fourier transformation (DFT) is defined as follows: \[ X_k = \sum_{j=0}^{N-1} x_j e^{-\frac{2\pi i}{N} j k} \] Where:
   • \(k\) is the frequency component
   • \(x_0,...,x_{N-1}\) are the values of the input time series
   • \(N\) is the number of non-missing values in the input time series
7. The Cooley-Tukey radix-2 decimation-in-time fast Fourier transformation (FFT) algorithm divides a DFT of size N into two overlapping DFTs of size $\frac{N}{2}$ at each of its stages using the following formula: \[ X_{k} = \begin{cases} E_k + \alpha \cdot O_k & \text{ if } k \lt \dfrac{N}{2} \\ E_{\left (k-\frac{N}{2} \right )} - \ \alpha \cdot O_{\left (k-\frac{N}{2} \right )} & \text{ if } k \geq \dfrac{N}{2} \end{cases} \] Where:
   • \(E_k\) is the DFT of the even-indicied values of the input time series, \(x_{2m} \left(x_0, x_2, \ldots, x_{N-2}\right)\)
   • \(O_k\) is the DFT of the odd-indicied values of the input time series, \(x_{2m+1} \left(x_1, x_3, \ldots, x_{N-2}\right)\)
   • \(\alpha = e^{ \left (-2 \pi i k /N \right )}\)
   • \(N\) is the number of non-missing values in the time series data
8. The unit frequency of the DFT is \(\frac{2\pi}{N}\), where \(N\) is the number of non-missing observations.

Exceptions

Exception Type	Condition
None	N/A

Requirements

Namespace	NumXLAPI
Class	SFSDK
Scope	Public
Lifetime	Static
Package	NumXLAPI.DLL

Examples