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Want combined Tile and Cascade Windows arrangement

Combined tile and cascade arrangement

1. window -s ch
   tile horizontally,then cascade each column

2. window -s cv
   tile vertically, cascade each column

3. window -s ct
   tile and cascade

Tile all windows in descending sequence

1. window -s th3 or window -s tv3
   tile first by window type(workbook->excel->graph->matrix->layout-notes),then by name descending
2. window -s th4 or window -s tv4
   tile by window name descending

note: the above descending mode (3,4) and ascending mode(1,2) also support for window -s ch/cv/ct.

We added following labtalk functions for signal processing:

1. fftc

vector<complex> fftc(vector<complex> cx)

It calculates the complex FFT result for given cx. We should use different algorithms depending on whether cx is real.
If cx's size is n, then output size is also n. (shift should be off.)

2. fftmag

vector fftmag(vector<complex> cx, int side=1 )

It can be used to calculate magnitude from FFT complex result. side=1 for one-sided by default, side=2 for two-sided and shift.

3. fftamp

vector fftamp(vector<complex> cx, int side=1 )

It can be used to calculate amplitude from FFT complex result. side=1 for one-sided by default, side=2 for two-sided and shift.

4. fftphase

vector fftphase(vector<complex> cx, int side=1, int unwrap=1, int unit=1 )

It can be used to calculate amplitude from FFT complex result.
side=1 for one-sided by default, side=2 for two-sided and shift.
unwrap=0 not unwrap phase angle, 1 for unwrap by default.
unit=1 for degrees unit by default, 0 for radians unit.

5. ifftshift

vector<complex> ifftshift(vector<complex> cx)

When fft result is shifted, to do ifft, we need unshift the result first.

6. invfft

vector<complex> invfft(vector<complex> cx)

Compute inverse FFT from fft result. If input size is n, output size is n.

7. fftfreq

vector fftfreq(double time, int n, int side=1, int shift=1)

Calculate frequencies for FFT results, the original result is time*data(0,n-1)
time: sampling interval
n: signal size
side: 1 for one-sided(by default), 2 for two-sided
shift: 0 for no-shift, and 1 for shift(by default), it is used for two-sided.
Return frequencies, two-sided size is n, one-sided size is ceil((n+1)/2)

8. fftshift

vector<complex> fftshift(vector<complex> cx)

It can be used to shift FFT results or frequency.

9. windata

vector windata(int type, int n)

type=0 rectangle, 1: Welch, 2: Triangular, 3: Bartlett, 4: Hanning, 5: Hamming, 6: Blackman
n is size for the window.
Return a vector of size n.