How to generate matrix in MATLAB

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charu shree
charu shree on 26 Aug 2023
Commented: Star Strider on 26 Aug 2023
Hello all, In my research work, I came across the following matrix, where and . My query is I am not getting how to generate this matrix in MATLAB.
Any help in this regard will be highly appreciated.

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Accepted Answer

Star Strider
Star Strider on 26 Aug 2023
Ran in:
Try this —
N = 32;
C = 33;
Wc = exp((1j*2*pi)/C)
Wc = 0.9819 + 0.1893i
P = ones(N+1,C);
P(2:end,2:end) = Wc.^((1:N)'*(1:C-1))
P =
Columns 1 through 10 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 0.9819 + 0.1893i 0.9284 + 0.3717i 0.8413 + 0.5406i 0.7237 + 0.6901i 0.5801 + 0.8146i 0.4154 + 0.9096i 0.2358 + 0.9718i 0.0476 + 0.9989i -0.1423 + 0.9898i 1.0000 + 0.0000i 0.9284 + 0.3717i 0.7237 + 0.6901i 0.4154 + 0.9096i 0.0476 + 0.9989i -0.3271 + 0.9450i -0.6549 + 0.7557i -0.8888 + 0.4582i -0.9955 + 0.0951i -0.9595 - 0.2817i 1.0000 + 0.0000i 0.8413 + 0.5406i 0.4154 + 0.9096i -0.1423 + 0.9898i -0.6549 + 0.7557i -0.9595 + 0.2817i -0.9595 - 0.2817i -0.6549 - 0.7557i -0.1423 - 0.9898i 0.4154 - 0.9096i 1.0000 + 0.0000i 0.7237 + 0.6901i 0.0476 + 0.9989i -0.6549 + 0.7557i -0.9955 + 0.0951i -0.7861 - 0.6182i -0.1423 - 0.9898i 0.5801 - 0.8146i 0.9819 - 0.1893i 0.8413 + 0.5406i 1.0000 + 0.0000i 0.5801 + 0.8146i -0.3271 + 0.9450i -0.9595 + 0.2817i -0.7861 - 0.6182i 0.0476 - 0.9989i 0.8413 - 0.5406i 0.9284 + 0.3717i 0.2358 + 0.9718i -0.6549 + 0.7557i 1.0000 + 0.0000i 0.4154 + 0.9096i -0.6549 + 0.7557i -0.9595 - 0.2817i -0.1423 - 0.9898i 0.8413 - 0.5406i 0.8413 + 0.5406i -0.1423 + 0.9898i -0.9595 + 0.2817i -0.6549 - 0.7557i 1.0000 + 0.0000i 0.2358 + 0.9718i -0.8888 + 0.4582i -0.6549 - 0.7557i 0.5801 - 0.8146i 0.9284 + 0.3717i -0.1423 + 0.9898i -0.9955 + 0.0951i -0.3271 - 0.9450i 0.8413 - 0.5406i 1.0000 + 0.0000i 0.0476 + 0.9989i -0.9955 + 0.0951i -0.1423 - 0.9898i 0.9819 - 0.1893i 0.2358 + 0.9718i -0.9595 + 0.2817i -0.3271 - 0.9450i 0.9284 - 0.3717i 0.4154 + 0.9096i 1.0000 + 0.0000i -0.1423 + 0.9898i -0.9595 - 0.2817i 0.4154 - 0.9096i 0.8413 + 0.5406i -0.6549 + 0.7557i -0.6549 - 0.7557i 0.8413 - 0.5406i 0.4154 + 0.9096i -0.9595 + 0.2817i 1.0000 + 0.0000i -0.3271 + 0.9450i -0.7861 - 0.6182i 0.8413 - 0.5406i 0.2358 + 0.9718i -0.9955 - 0.0951i 0.4154 - 0.9096i 0.7237 + 0.6901i -0.8888 + 0.4582i -0.1423 - 0.9898i 1.0000 + 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i 1.0000 + 0.0000i -0.6549 + 0.7557i -0.1423 - 0.9898i 0.8413 + 0.5406i -0.9595 + 0.2817i 0.4154 - 0.9096i 0.4154 + 0.9096i -0.9595 - 0.2817i 0.8413 - 0.5406i -0.1423 + 0.9898i 1.0000 + 0.0000i -0.7861 + 0.6182i 0.2358 - 0.9718i 0.4154 + 0.9096i -0.8888 - 0.4582i 0.9819 - 0.1893i -0.6549 + 0.7557i 0.0476 - 0.9989i 0.5801 + 0.8146i -0.9595 - 0.2817i 1.0000 + 0.0000i -0.8888 + 0.4582i 0.5801 - 0.8146i -0.1423 + 0.9898i -0.3271 - 0.9450i 0.7237 + 0.6901i -0.9595 - 0.2817i 0.9819 - 0.1893i -0.7861 + 0.6182i 0.4154 - 0.9096i 1.0000 + 0.0000i -0.9595 + 0.2817i 0.8413 - 0.5406i -0.6549 + 0.7557i 0.4154 - 0.9096i -0.1423 + 0.9898i -0.1423 - 0.9898i 0.4154 + 0.9096i -0.6549 - 0.7557i 0.8413 + 0.5406i 1.0000 + 0.0000i -0.9955 + 0.0951i 0.9819 - 0.1893i -0.9595 + 0.2817i 0.9284 - 0.3717i -0.8888 + 0.4582i 0.8413 - 0.5406i -0.7861 + 0.6182i 0.7237 - 0.6901i -0.6549 + 0.7557i 1.0000 + 0.0000i -0.9955 - 0.0951i 0.9819 + 0.1893i -0.9595 - 0.2817i 0.9284 + 0.3717i -0.8888 - 0.4582i 0.8413 + 0.5406i -0.7861 - 0.6182i 0.7237 + 0.6901i -0.6549 - 0.7557i 1.0000 + 0.0000i -0.9595 - 0.2817i 0.8413 + 0.5406i -0.6549 - 0.7557i 0.4154 + 0.9096i -0.1423 - 0.9898i -0.1423 + 0.9898i 0.4154 - 0.9096i -0.6549 + 0.7557i 0.8413 - 0.5406i 1.0000 + 0.0000i -0.8888 - 0.4582i 0.5801 + 0.8146i -0.1423 - 0.9898i -0.3271 + 0.9450i 0.7237 - 0.6901i -0.9595 + 0.2817i 0.9819 + 0.1893i -0.7861 - 0.6182i 0.4154 + 0.9096i 1.0000 + 0.0000i -0.7861 - 0.6182i 0.2358 + 0.9718i 0.4154 - 0.9096i -0.8888 + 0.4582i 0.9819 + 0.1893i -0.6549 - 0.7557i 0.0476 + 0.9989i 0.5801 - 0.8146i -0.9595 + 0.2817i 1.0000 + 0.0000i -0.6549 - 0.7557i -0.1423 + 0.9898i 0.8413 - 0.5406i -0.9595 - 0.2817i 0.4154 + 0.9096i 0.4154 - 0.9096i -0.9595 + 0.2817i 0.8413 + 0.5406i -0.1423 - 0.9898i 1.0000 + 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i 1.0000 + 0.0000i -0.3271 - 0.9450i -0.7861 + 0.6182i 0.8413 + 0.5406i 0.2358 - 0.9718i -0.9955 + 0.0951i 0.4154 + 0.9096i 0.7237 - 0.6901i -0.8888 - 0.4582i -0.1423 + 0.9898i 1.0000 + 0.0000i -0.1423 - 0.9898i -0.9595 + 0.2817i 0.4154 + 0.9096i 0.8413 - 0.5406i -0.6549 - 0.7557i -0.6549 + 0.7557i 0.8413 + 0.5406i 0.4154 - 0.9096i -0.9595 - 0.2817i 1.0000 + 0.0000i 0.0476 - 0.9989i -0.9955 - 0.0951i -0.1423 + 0.9898i 0.9819 + 0.1893i 0.2358 - 0.9718i -0.9595 - 0.2817i -0.3271 + 0.9450i 0.9284 + 0.3717i 0.4154 - 0.9096i 1.0000 + 0.0000i 0.2358 - 0.9718i -0.8888 - 0.4582i -0.6549 + 0.7557i 0.5801 + 0.8146i 0.9284 - 0.3717i -0.1423 - 0.9898i -0.9955 - 0.0951i -0.3271 + 0.9450i 0.8413 + 0.5406i 1.0000 + 0.0000i 0.4154 - 0.9096i -0.6549 - 0.7557i -0.9595 + 0.2817i -0.1423 + 0.9898i 0.8413 + 0.5406i 0.8413 - 0.5406i -0.1423 - 0.9898i -0.9595 - 0.2817i -0.6549 + 0.7557i 1.0000 + 0.0000i 0.5801 - 0.8146i -0.3271 - 0.9450i -0.9595 - 0.2817i -0.7861 + 0.6182i 0.0476 + 0.9989i 0.8413 + 0.5406i 0.9284 - 0.3717i 0.2358 - 0.9718i -0.6549 - 0.7557i 1.0000 + 0.0000i 0.7237 - 0.6901i 0.0476 - 0.9989i -0.6549 - 0.7557i -0.9955 - 0.0951i -0.7861 + 0.6182i -0.1423 + 0.9898i 0.5801 + 0.8146i 0.9819 + 0.1893i 0.8413 - 0.5406i 1.0000 + 0.0000i 0.8413 - 0.5406i 0.4154 - 0.9096i -0.1423 - 0.9898i -0.6549 - 0.7557i -0.9595 - 0.2817i -0.9595 + 0.2817i -0.6549 + 0.7557i -0.1423 + 0.9898i 0.4154 + 0.9096i 1.0000 + 0.0000i 0.9284 - 0.3717i 0.7237 - 0.6901i 0.4154 - 0.9096i 0.0476 - 0.9989i -0.3271 - 0.9450i -0.6549 - 0.7557i -0.8888 - 0.4582i -0.9955 - 0.0951i -0.9595 + 0.2817i 1.0000 + 0.0000i 0.9819 - 0.1893i 0.9284 - 0.3717i 0.8413 - 0.5406i 0.7237 - 0.6901i 0.5801 - 0.8146i 0.4154 - 0.9096i 0.2358 - 0.9718i 0.0476 - 0.9989i -0.1423 - 0.9898i Columns 11 through 20 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i -0.3271 + 0.9450i -0.5000 + 0.8660i -0.6549 + 0.7557i -0.7861 + 0.6182i -0.8888 + 0.4582i -0.9595 + 0.2817i -0.9955 + 0.0951i -0.9955 - 0.0951i -0.9595 - 0.2817i -0.8888 - 0.4582i -0.7861 - 0.6182i -0.5000 - 0.8660i -0.1423 - 0.9898i 0.2358 - 0.9718i 0.5801 - 0.8146i 0.8413 - 0.5406i 0.9819 - 0.1893i 0.9819 + 0.1893i 0.8413 + 0.5406i 0.5801 + 0.8146i 0.8413 - 0.5406i 1.0000 - 0.0000i 0.8413 + 0.5406i 0.4154 + 0.9096i -0.1423 + 0.9898i -0.6549 + 0.7557i -0.9595 + 0.2817i -0.9595 - 0.2817i -0.6549 - 0.7557i -0.1423 - 0.9898i 0.2358 + 0.9718i -0.5000 + 0.8660i -0.9595 + 0.2817i -0.8888 - 0.4582i -0.3271 - 0.9450i 0.4154 - 0.9096i 0.9284 - 0.3717i 0.9284 + 0.3717i 0.4154 + 0.9096i -0.3271 + 0.9450i -0.9955 - 0.0951i -0.5000 - 0.8660i 0.4154 - 0.9096i 0.9819 - 0.1893i 0.7237 + 0.6901i -0.1423 + 0.9898i -0.8888 + 0.4582i -0.8888 - 0.4582i -0.1423 - 0.9898i 0.7237 - 0.6901i 0.4154 - 0.9096i 1.0000 - 0.0000i 0.4154 + 0.9096i -0.6549 + 0.7557i -0.9595 - 0.2817i -0.1423 - 0.9898i 0.8413 - 0.5406i 0.8413 + 0.5406i -0.1423 + 0.9898i -0.9595 + 0.2817i 0.7237 + 0.6901i -0.5000 + 0.8660i -0.9595 - 0.2817i 0.0476 - 0.9989i 0.9819 - 0.1893i 0.4154 + 0.9096i -0.7861 + 0.6182i -0.7861 - 0.6182i 0.4154 - 0.9096i 0.9819 + 0.1893i -0.8888 + 0.4582i -0.5000 - 0.8660i 0.8413 - 0.5406i 0.5801 + 0.8146i -0.7861 + 0.6182i -0.6549 - 0.7557i 0.7237 - 0.6901i 0.7237 + 0.6901i -0.6549 + 0.7557i -0.7861 - 0.6182i -0.1423 - 0.9898i 1.0000 - 0.0000i -0.1423 + 0.9898i -0.9595 - 0.2817i 0.4154 - 0.9096i 0.8413 + 0.5406i -0.6549 + 0.7557i -0.6549 - 0.7557i 0.8413 - 0.5406i 0.4154 + 0.9096i 0.9819 + 0.1893i -0.5000 + 0.8660i -0.6549 - 0.7557i 0.9284 - 0.3717i 0.0476 + 0.9989i -0.9595 - 0.2817i 0.5801 - 0.8146i 0.5801 + 0.8146i -0.9595 + 0.2817i 0.0476 - 0.9989i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.6549 - 0.7557i 1.0000 - 0.0000i -0.6549 + 0.7557i -0.1423 - 0.9898i 0.8413 + 0.5406i -0.9595 + 0.2817i 0.4154 - 0.9096i 0.4154 + 0.9096i -0.9595 - 0.2817i 0.8413 - 0.5406i 0.9284 - 0.3717i -0.5000 + 0.8660i -0.1423 - 0.9898i 0.7237 + 0.6901i -0.9955 - 0.0951i 0.8413 - 0.5406i -0.3271 + 0.9450i -0.3271 - 0.9450i 0.8413 + 0.5406i -0.9955 + 0.0951i 0.0476 + 0.9989i -0.5000 - 0.8660i 0.8413 + 0.5406i -0.9955 - 0.0951i 0.9284 - 0.3717i -0.6549 + 0.7557i 0.2358 - 0.9718i 0.2358 + 0.9718i -0.6549 - 0.7557i 0.9284 + 0.3717i -0.9595 - 0.2817i 1.0000 - 0.0000i -0.9595 + 0.2817i 0.8413 - 0.5406i -0.6549 + 0.7557i 0.4154 - 0.9096i -0.1423 + 0.9898i -0.1423 - 0.9898i 0.4154 + 0.9096i -0.6549 - 0.7557i 0.5801 - 0.8146i -0.5000 + 0.8660i 0.4154 - 0.9096i -0.3271 + 0.9450i 0.2358 - 0.9718i -0.1423 + 0.9898i 0.0476 - 0.9989i 0.0476 + 0.9989i -0.1423 - 0.9898i 0.2358 + 0.9718i 0.5801 + 0.8146i -0.5000 - 0.8660i 0.4154 + 0.9096i -0.3271 - 0.9450i 0.2358 + 0.9718i -0.1423 - 0.9898i 0.0476 + 0.9989i 0.0476 - 0.9989i -0.1423 + 0.9898i 0.2358 - 0.9718i -0.9595 + 0.2817i 1.0000 - 0.0000i -0.9595 - 0.2817i 0.8413 + 0.5406i -0.6549 - 0.7557i 0.4154 + 0.9096i -0.1423 - 0.9898i -0.1423 + 0.9898i 0.4154 - 0.9096i -0.6549 + 0.7557i 0.0476 - 0.9989i -0.5000 + 0.8660i 0.8413 - 0.5406i -0.9955 + 0.0951i 0.9284 + 0.3717i -0.6549 - 0.7557i 0.2358 + 0.9718i 0.2358 - 0.9718i -0.6549 + 0.7557i 0.9284 - 0.3717i 0.9284 + 0.3717i -0.5000 - 0.8660i -0.1423 + 0.9898i 0.7237 - 0.6901i -0.9955 + 0.0951i 0.8413 + 0.5406i -0.3271 - 0.9450i -0.3271 + 0.9450i 0.8413 - 0.5406i -0.9955 - 0.0951i -0.6549 + 0.7557i 1.0000 - 0.0000i -0.6549 - 0.7557i -0.1423 + 0.9898i 0.8413 - 0.5406i -0.9595 - 0.2817i 0.4154 + 0.9096i 0.4154 - 0.9096i -0.9595 + 0.2817i 0.8413 + 0.5406i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i 0.9819 - 0.1893i -0.5000 - 0.8660i -0.6549 + 0.7557i 0.9284 + 0.3717i 0.0476 - 0.9989i -0.9595 + 0.2817i 0.5801 + 0.8146i 0.5801 - 0.8146i -0.9595 - 0.2817i 0.0476 + 0.9989i -0.1423 + 0.9898i 1.0000 - 0.0000i -0.1423 - 0.9898i -0.9595 + 0.2817i 0.4154 + 0.9096i 0.8413 - 0.5406i -0.6549 - 0.7557i -0.6549 + 0.7557i 0.8413 + 0.5406i 0.4154 - 0.9096i -0.8888 - 0.4582i -0.5000 + 0.8660i 0.8413 + 0.5406i 0.5801 - 0.8146i -0.7861 - 0.6182i -0.6549 + 0.7557i 0.7237 + 0.6901i 0.7237 - 0.6901i -0.6549 - 0.7557i -0.7861 + 0.6182i 0.7237 - 0.6901i -0.5000 - 0.8660i -0.9595 + 0.2817i 0.0476 + 0.9989i 0.9819 + 0.1893i 0.4154 - 0.9096i -0.7861 - 0.6182i -0.7861 + 0.6182i 0.4154 + 0.9096i 0.9819 - 0.1893i 0.4154 + 0.9096i 1.0000 - 0.0000i 0.4154 - 0.9096i -0.6549 - 0.7557i -0.9595 + 0.2817i -0.1423 + 0.9898i 0.8413 + 0.5406i 0.8413 - 0.5406i -0.1423 - 0.9898i -0.9595 - 0.2817i -0.9955 + 0.0951i -0.5000 + 0.8660i 0.4154 + 0.9096i 0.9819 + 0.1893i 0.7237 - 0.6901i -0.1423 - 0.9898i -0.8888 - 0.4582i -0.8888 + 0.4582i -0.1423 + 0.9898i 0.7237 + 0.6901i 0.2358 - 0.9718i -0.5000 - 0.8660i -0.9595 - 0.2817i -0.8888 + 0.4582i -0.3271 + 0.9450i 0.4154 + 0.9096i 0.9284 + 0.3717i 0.9284 - 0.3717i 0.4154 - 0.9096i -0.3271 - 0.9450i 0.8413 + 0.5406i 1.0000 - 0.0000i 0.8413 - 0.5406i 0.4154 - 0.9096i -0.1423 - 0.9898i -0.6549 - 0.7557i -0.9595 - 0.2817i -0.9595 + 0.2817i -0.6549 + 0.7557i -0.1423 + 0.9898i -0.7861 + 0.6182i -0.5000 + 0.8660i -0.1423 + 0.9898i 0.2358 + 0.9718i 0.5801 + 0.8146i 0.8413 + 0.5406i 0.9819 + 0.1893i 0.9819 - 0.1893i 0.8413 - 0.5406i 0.5801 - 0.8146i -0.3271 - 0.9450i -0.5000 - 0.8660i -0.6549 - 0.7557i -0.7861 - 0.6182i -0.8888 - 0.4582i -0.9595 - 0.2817i -0.9955 - 0.0951i -0.9955 + 0.0951i -0.9595 + 0.2817i -0.8888 + 0.4582i Columns 21 through 30 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i -0.7861 - 0.6182i -0.6549 - 0.7557i -0.5000 - 0.8660i -0.3271 - 0.9450i -0.1423 - 0.9898i 0.0476 - 0.9989i 0.2358 - 0.9718i 0.4154 - 0.9096i 0.5801 - 0.8146i 0.7237 - 0.6901i 0.2358 + 0.9718i -0.1423 + 0.9898i -0.5000 + 0.8660i -0.7861 + 0.6182i -0.9595 + 0.2817i -0.9955 - 0.0951i -0.8888 - 0.4582i -0.6549 - 0.7557i -0.3271 - 0.9450i 0.0476 - 0.9989i 0.4154 - 0.9096i 0.8413 - 0.5406i 1.0000 - 0.0000i 0.8413 + 0.5406i 0.4154 + 0.9096i -0.1423 + 0.9898i -0.6549 + 0.7557i -0.9595 + 0.2817i -0.9595 - 0.2817i -0.6549 - 0.7557i -0.8888 + 0.4582i -0.9595 - 0.2817i -0.5000 - 0.8660i 0.2358 - 0.9718i 0.8413 - 0.5406i 0.9819 + 0.1893i 0.5801 + 0.8146i -0.1423 + 0.9898i -0.7861 + 0.6182i -0.9955 - 0.0951i 0.9819 + 0.1893i 0.4154 + 0.9096i -0.5000 + 0.8660i -0.9955 + 0.0951i -0.6549 - 0.7557i 0.2358 - 0.9718i 0.9284 - 0.3717i 0.8413 + 0.5406i 0.0476 + 0.9989i -0.7861 + 0.6182i -0.6549 - 0.7557i 0.4154 - 0.9096i 1.0000 - 0.0000i 0.4154 + 0.9096i -0.6549 + 0.7557i -0.9595 - 0.2817i -0.1423 - 0.9898i 0.8413 - 0.5406i 0.8413 + 0.5406i -0.1423 + 0.9898i 0.0476 + 0.9989i -0.9595 + 0.2817i -0.5000 - 0.8660i 0.7237 - 0.6901i 0.8413 + 0.5406i -0.3271 + 0.9450i -0.9955 - 0.0951i -0.1423 - 0.9898i 0.9284 - 0.3717i 0.5801 + 0.8146i 0.5801 - 0.8146i 0.8413 + 0.5406i -0.5000 + 0.8660i -0.8888 - 0.4582i 0.4154 - 0.9096i 0.9284 + 0.3717i -0.3271 + 0.9450i -0.9595 - 0.2817i 0.2358 - 0.9718i 0.9819 + 0.1893i -0.9595 + 0.2817i -0.1423 - 0.9898i 1.0000 - 0.0000i -0.1423 + 0.9898i -0.9595 - 0.2817i 0.4154 - 0.9096i 0.8413 + 0.5406i -0.6549 + 0.7557i -0.6549 - 0.7557i 0.8413 - 0.5406i 0.9284 + 0.3717i -0.6549 + 0.7557i -0.5000 - 0.8660i 0.9819 - 0.1893i -0.1423 + 0.9898i -0.8888 - 0.4582i 0.7237 - 0.6901i 0.4154 + 0.9096i -0.9955 + 0.0951i 0.2358 - 0.9718i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i -0.1423 + 0.9898i -0.6549 - 0.7557i 1.0000 - 0.0000i -0.6549 + 0.7557i -0.1423 - 0.9898i 0.8413 + 0.5406i -0.9595 + 0.2817i 0.4154 - 0.9096i 0.4154 + 0.9096i -0.9595 - 0.2817i 0.7237 - 0.6901i -0.1423 + 0.9898i -0.5000 - 0.8660i 0.9284 + 0.3717i -0.9595 + 0.2817i 0.5801 - 0.8146i 0.0476 + 0.9989i -0.6549 - 0.7557i 0.9819 + 0.1893i -0.8888 + 0.4582i -0.9955 + 0.0951i 0.8413 - 0.5406i -0.5000 + 0.8660i 0.0476 - 0.9989i 0.4154 + 0.9096i -0.7861 - 0.6182i 0.9819 + 0.1893i -0.9595 + 0.2817i 0.7237 - 0.6901i -0.3271 + 0.9450i 0.8413 + 0.5406i -0.9595 - 0.2817i 1.0000 - 0.0000i -0.9595 + 0.2817i 0.8413 - 0.5406i -0.6549 + 0.7557i 0.4154 - 0.9096i -0.1423 + 0.9898i -0.1423 - 0.9898i 0.4154 + 0.9096i -0.3271 - 0.9450i 0.4154 + 0.9096i -0.5000 - 0.8660i 0.5801 + 0.8146i -0.6549 - 0.7557i 0.7237 + 0.6901i -0.7861 - 0.6182i 0.8413 + 0.5406i -0.8888 - 0.4582i 0.9284 + 0.3717i -0.3271 + 0.9450i 0.4154 - 0.9096i -0.5000 + 0.8660i 0.5801 - 0.8146i -0.6549 + 0.7557i 0.7237 - 0.6901i -0.7861 + 0.6182i 0.8413 - 0.5406i -0.8888 + 0.4582i 0.9284 - 0.3717i 0.8413 - 0.5406i -0.9595 + 0.2817i 1.0000 - 0.0000i -0.9595 - 0.2817i 0.8413 + 0.5406i -0.6549 - 0.7557i 0.4154 + 0.9096i -0.1423 - 0.9898i -0.1423 + 0.9898i 0.4154 - 0.9096i -0.9955 - 0.0951i 0.8413 + 0.5406i -0.5000 - 0.8660i 0.0476 + 0.9989i 0.4154 - 0.9096i -0.7861 + 0.6182i 0.9819 - 0.1893i -0.9595 - 0.2817i 0.7237 + 0.6901i -0.3271 - 0.9450i 0.7237 + 0.6901i -0.1423 - 0.9898i -0.5000 + 0.8660i 0.9284 - 0.3717i -0.9595 - 0.2817i 0.5801 + 0.8146i 0.0476 - 0.9989i -0.6549 + 0.7557i 0.9819 - 0.1893i -0.8888 - 0.4582i -0.1423 - 0.9898i -0.6549 + 0.7557i 1.0000 - 0.0000i -0.6549 - 0.7557i -0.1423 + 0.9898i 0.8413 - 0.5406i -0.9595 - 0.2817i 0.4154 + 0.9096i 0.4154 - 0.9096i -0.9595 + 0.2817i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 0.9284 - 0.3717i -0.6549 - 0.7557i -0.5000 + 0.8660i 0.9819 + 0.1893i -0.1423 - 0.9898i -0.8888 + 0.4582i 0.7237 + 0.6901i 0.4154 - 0.9096i -0.9955 - 0.0951i 0.2358 + 0.9718i -0.9595 - 0.2817i -0.1423 + 0.9898i 1.0000 - 0.0000i -0.1423 - 0.9898i -0.9595 + 0.2817i 0.4154 + 0.9096i 0.8413 - 0.5406i -0.6549 - 0.7557i -0.6549 + 0.7557i 0.8413 + 0.5406i 0.5801 + 0.8146i 0.8413 - 0.5406i -0.5000 - 0.8660i -0.8888 + 0.4582i 0.4154 + 0.9096i 0.9284 - 0.3717i -0.3271 - 0.9450i -0.9595 + 0.2817i 0.2358 + 0.9718i 0.9819 - 0.1893i 0.0476 - 0.9989i -0.9595 - 0.2817i -0.5000 + 0.8660i 0.7237 + 0.6901i 0.8413 - 0.5406i -0.3271 - 0.9450i -0.9955 + 0.0951i -0.1423 + 0.9898i 0.9284 + 0.3717i 0.5801 - 0.8146i -0.6549 + 0.7557i 0.4154 + 0.9096i 1.0000 - 0.0000i 0.4154 - 0.9096i -0.6549 - 0.7557i -0.9595 + 0.2817i -0.1423 + 0.9898i 0.8413 + 0.5406i 0.8413 - 0.5406i -0.1423 - 0.9898i 0.9819 - 0.1893i 0.4154 - 0.9096i -0.5000 - 0.8660i -0.9955 - 0.0951i -0.6549 + 0.7557i 0.2358 + 0.9718i 0.9284 + 0.3717i 0.8413 - 0.5406i 0.0476 - 0.9989i -0.7861 - 0.6182i -0.8888 - 0.4582i -0.9595 + 0.2817i -0.5000 + 0.8660i 0.2358 + 0.9718i 0.8413 + 0.5406i 0.9819 - 0.1893i 0.5801 - 0.8146i -0.1423 - 0.9898i -0.7861 - 0.6182i -0.9955 + 0.0951i 0.4154 + 0.9096i 0.8413 + 0.5406i 1.0000 - 0.0000i 0.8413 - 0.5406i 0.4154 - 0.9096i -0.1423 - 0.9898i -0.6549 - 0.7557i -0.9595 - 0.2817i -0.9595 + 0.2817i -0.6549 + 0.7557i 0.2358 - 0.9718i -0.1423 - 0.9898i -0.5000 - 0.8660i -0.7861 - 0.6182i -0.9595 - 0.2817i -0.9955 + 0.0951i -0.8888 + 0.4582i -0.6549 + 0.7557i -0.3271 + 0.9450i 0.0476 + 0.9989i -0.7861 + 0.6182i -0.6549 + 0.7557i -0.5000 + 0.8660i -0.3271 + 0.9450i -0.1423 + 0.9898i 0.0476 + 0.9989i 0.2358 + 0.9718i 0.4154 + 0.9096i 0.5801 + 0.8146i 0.7237 + 0.6901i Columns 31 through 33 1.0000 + 0.0000i 1.0000 + 0.0000i 1.0000 + 0.0000i 0.8413 - 0.5406i 0.9284 - 0.3717i 0.9819 - 0.1893i 0.4154 - 0.9096i 0.7237 - 0.6901i 0.9284 - 0.3717i -0.1423 - 0.9898i 0.4154 - 0.9096i 0.8413 - 0.5406i -0.6549 - 0.7557i 0.0476 - 0.9989i 0.7237 - 0.6901i -0.9595 - 0.2817i -0.3271 - 0.9450i 0.5801 - 0.8146i -0.9595 + 0.2817i -0.6549 - 0.7557i 0.4154 - 0.9096i -0.6549 + 0.7557i -0.8888 - 0.4582i 0.2358 - 0.9718i -0.1423 + 0.9898i -0.9955 - 0.0951i 0.0476 - 0.9989i 0.4154 + 0.9096i -0.9595 + 0.2817i -0.1423 - 0.9898i 0.8413 + 0.5406i -0.7861 + 0.6182i -0.3271 - 0.9450i 1.0000 - 0.0000i -0.5000 + 0.8660i -0.5000 - 0.8660i 0.8413 - 0.5406i -0.1423 + 0.9898i -0.6549 - 0.7557i 0.4154 - 0.9096i 0.2358 + 0.9718i -0.7861 - 0.6182i -0.1423 - 0.9898i 0.5801 + 0.8146i -0.8888 - 0.4582i -0.6549 - 0.7557i 0.8413 + 0.5406i -0.9595 - 0.2817i -0.9595 - 0.2817i 0.9819 + 0.1893i -0.9955 - 0.0951i -0.9595 + 0.2817i 0.9819 - 0.1893i -0.9955 + 0.0951i -0.6549 + 0.7557i 0.8413 - 0.5406i -0.9595 + 0.2817i -0.1423 + 0.9898i 0.5801 - 0.8146i -0.8888 + 0.4582i 0.4154 + 0.9096i 0.2358 - 0.9718i -0.7861 + 0.6182i 0.8413 + 0.5406i -0.1423 - 0.9898i -0.6549 + 0.7557i 1.0000 - 0.0000i -0.5000 - 0.8660i -0.5000 + 0.8660i 0.8413 - 0.5406i -0.7861 - 0.6182i -0.3271 + 0.9450i 0.4154 - 0.9096i -0.9595 - 0.2817i -0.1423 + 0.9898i -0.1423 - 0.9898i -0.9955 + 0.0951i 0.0476 + 0.9989i -0.6549 - 0.7557i -0.8888 + 0.4582i 0.2358 + 0.9718i -0.9595 - 0.2817i -0.6549 + 0.7557i 0.4154 + 0.9096i -0.9595 + 0.2817i -0.3271 + 0.9450i 0.5801 + 0.8146i -0.6549 + 0.7557i 0.0476 + 0.9989i 0.7237 + 0.6901i -0.1423 + 0.9898i 0.4154 + 0.9096i 0.8413 + 0.5406i 0.4154 + 0.9096i 0.7237 + 0.6901i 0.9284 + 0.3717i 0.8413 + 0.5406i 0.9284 + 0.3717i 0.9819 + 0.1893i
The approach is to first create the ones matrix for ‘P’, then fill it all except the first row and first column with the matrix of ‘W’ raised to the ‘(1:N)'*(1:C-1)’ power (which is how I interpreted it). The entire matrix appears to be complex, however the first row and column are real and equal to 1.
.
  2 Comments
charu shree
charu shree on 26 Aug 2023
Thank you so much sir for your detailed response....
Star Strider
Star Strider on 26 Aug 2023
As always, my pleasure!

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More Answers (1)

Voss
Voss on 26 Aug 2023 
N = 32;
C = 33;
P = exp(1j*2*pi/C.*((0:N).'.*(0:C-1)))

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