Stem Construction Utility

629aa651-4eca-4f18-ba2d-1b2236586045 5 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Fourier spectrum stem style

Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem N vy length : i 1 N range q i el 3 : q N el 2 : 21 line for 11 line i 1 N range v i el i : for i 1 N range S 3 i * el vy i el : for u q v replicate : V u S augment : V V 3 V rows 12 submatrix : 71 line :

Data

XY data_1 data_2 data_3 data_4 stack :

X XY 1 col :

Y XY 2 col :

Y Y 110011 submatrix :

t0 1 time :

fft(Y)

data_1 1 0.132 - 2 0.11 - 3 0.045 4 0.0045 5 0.138 - 6 0.467 7 0.5 8 0.78 9 1.342 10 0.993 11 1.105 12 1.119 13 1.18 14 1.143 15 0.655 16 1.008 17 0.771 18 1.208 19 0.938 20 0.783 21 0.734 22 0.763 23 1.044 24 0.754 25 0.797 252 mat :

data_2 26 1.086 27 0.426 28 0.563 29 0.814 30 0.665 31 0.561 - 32 0.429 - 33 0.187 34 0.153 - 35 0.422 - 36 0.127 - 37 0.018 - 38 0.247 - 39 0.422 - 40 0.738 - 41 0.711 - 42 0.863 - 43 0.769 - 44 0.485 - 45 0.79 - 46 0.737 - 47 0.708 - 48 0.965 - 49 0.899 - 50 0.947 - 252 mat :

data_3 51 0.871 - 52 1.138 - 53 1.191 - 54 0.046 - 55 1.016 - 56 1.275 - 57 0.617 - 58 0.908 - 59 1.09 - 60 0.972 - 61 0.594 - 62 0.5 - 63 0.346 - 64 0.191 - 65 0.177 - 66 0.362 - 67 0.547 - 68 0.455 69 0.417 70 0.129 - 71 0.352 72 0.906 73 0.386 74 0.047 - 75 0.214 252 mat :

data_4 76 0.309 77 0.615 78 0.846 79 0.698 80 0.819 81 1.113 82 1.042 83 1.114 84 0.653 85 0.667 86 0.657 87 0.846 88 0.547 89 0.053 90 1.244 91 1.046 92 0.793 93 0.383 94 0.335 95 0.272 96 0.537 97 0.248 98 0.67 99 0.226 - 100 0.208 252 mat :

Fourier complex  from sampled  Y vector ... [even/odd] Y fft N Y length : n 0 N range D n 1 + el 1 N sqrt / Y k 1 + el e i 2 π * n * N / (* k *^* (k 0 N 1 - sum * eval : for D 31 line :

L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx - (dx i * + : for U 41 line :

Export complex for subuse F Y fft :

L 5 - : H 5 : N F length : U L H N xd : 41 line

Vectorise 'F' to get spectrum data Ω F mat2sys abs sys2mat : U Ω augment 21 line :

XY data_1 data_2 data_3 data_4 stack :

X XY 1 col :

Y XY 2 col :

Y Y 110011 submatrix :

t0 1 time :

fft(Y)

Fourier complex  from sampled  Y vector ... [even/odd] Y fft N Y length : n 0 N range D n 1 + el 1 N sqrt / Y k 1 + el e i 2 π * n * N / (* k *^* (k 0 N 1 - sum * eval : for D 31 line :

L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx - (dx i * + : for U 41 line :

Export complex for subuse F Y fft :

L 5 - : H 5 : N F length : U L H N xd : 41 line

Vectorise 'F' to get spectrum data Ω F mat2sys abs sys2mat : U Ω augment 21 line :

Collect the project fft data 2 col : DC 1 - 01 - fft 1 el 0 fft 1 el 0042 mat : vy data 2 col : Spectrum vy stem : 41 line

<= DC ... isolate/highlight the DC component

Unscaled spectrum ... random sampled data

Spectrum DC 2 1 sys

Centereded spectrum

data

View the noisy sampled data.

data_1 data_2 data_3 data_4 4 1 sys

1 time t0 - 7 sec *