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POWhy do I get rows of zeros in my 2D fft?
 

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  1. POWhy do I get rows of zeros in my 2D fft?
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    <p>I am trying to replicate the results from a paper.</p> <p>"Two-dimensional Fourier Transform (2D-FT) in space and time along sections of constant latitude (east-west) and longitude (north-south) were used to characterize the spectrum of the simulated flux variability south of 40degS." - Lenton et al(2006) The figures published show "the log of the variance of the 2D-FT".</p> <p>I have tried to create an array consisting of the seasonal cycle of similar data as well as the noise. I have defined the noise as the original array minus the signal array.</p> <p>Here is the code that I used to plot the 2D-FT of the signal array averaged in latitude:</p> <pre><code>import numpy as np from numpy import ma from matplotlib import pyplot as plt from Scientific.IO.NetCDF import NetCDFFile ### input directory indir = '/home/nicholas/data/' ### get the flux data which is in ### [time(5day ave for 10 years),latitude,longitude] nc = NetCDFFile(indir + 'CFLX_2000_2009.nc','r') cflux_southern_ocean = nc.variables['Cflx'][:,10:50,:] cflux_southern_ocean = ma.masked_values(cflux_southern_ocean,1e+20) # mask land nc.close() cflux = cflux_southern_ocean*1e08 # change units of data from mmol/m^2/s ### create an array that consists of the seasonal signal fro each pixel year_stack = np.split(cflux, 10, axis=0) year_stack = np.array(year_stack) signal_array = np.tile(np.mean(year_stack, axis=0), (10, 1, 1)) signal_array = ma.masked_where(signal_array &gt; 1e20, signal_array) # need to mask ### average the array over latitude(or longitude) signal_time_lon = ma.mean(signal_array, axis=1) ### do a 2D Fourier Transform of the time/space image ft = np.fft.fft2(signal_time_lon) mgft = np.abs(ft) ps = mgft**2 log_ps = np.log(mgft) log_mgft= np.log(mgft) </code></pre> <p>Every second row of the ft consists completely of zeros. Why is this? Would it be acceptable to add a randomly small number to the signal to avoid this.</p> <pre><code>signal_time_lon = signal_time_lon + np.random.randint(0,9,size=(730, 182))*1e-05 </code></pre> <p>EDIT: Adding images and clarify meaning</p> <p>The output of rfft2 still appears to be a complex array. Using fftshift shifts the edges of the image to the centre; I still have a power spectrum regardless. I expect that the reason that I get rows of zeros is that I have re-created the timeseries for each pixel. The ft[0, 0] pixel contains the mean of the signal. So the ft[1, 0] corresponds to a sinusoid with one cycle over the entire signal in the rows of the starting image.</p> <p>Here are is the starting image using following code: <img src="https://i.stack.imgur.com/PLStW.png" alt="Starting image"></p> <pre><code>plt.pcolormesh(signal_time_lon); plt.colorbar(); plt.axis('tight') </code></pre> <p>Here is result using following code: <img src="https://i.stack.imgur.com/BNW9A.png" alt="enter image description here"></p> <pre><code>ft = np.fft.rfft2(signal_time_lon) mgft = np.abs(ft) ps = mgft**2 log_ps = np.log1p(mgft) plt.pcolormesh(log_ps); plt.colorbar(); plt.axis('tight') </code></pre> <p>It may not be clear in the image but it is only every second row that contains completely zeros. Every tenth pixel (log_ps[10, 0]) is a high value. The other pixels (log_ps[2, 0], log_ps[4, 0] etc) have very low values.</p>
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