I don’t frequently use FFT, so it still confounds every time I try to interpret the results from FFT, I’ll try to organize my understanding here…

INFORMATION ABOUT THE DATA FILE TO PROCESS

data = array of samples
data_pts = total samples in data file (number of samples/lines in data file)
data_srate = sampling rate (points per second)
data_stime = total time covered in seconds (data_pts / data_srate)

THE numpy.fft() FUNCTION AND THE RESULTS

fft_result = fft(data)
fft_freqs = fftfreq( len(fft_result) )

(fft_result has a real and imag part, but I’m focusing on the real part here)

len(fft_result) == len(data)

but this is mostly meaningless

fft_result[n] corresponds to fft_freqs[n]

PRECISION
The interval difference if fft_freqs equals the inverse of data_stime.
This interval has nothing to do with the number of samples which is what confused me most. I had expected that having 1024 samples per second would return a more precise frequency plotting versus 2 samples per second.
In other words, if the sampled time period is 10 seconds long. No matter if you have 2 or 100 samples per second, the intervals of the frequency ‘bins’ will be 0.1. The number of 0.1-bins depends on the number of samples. In this case, 2 samples per second will produce 20 bins ranging from -1.0 to 0.9; 100 samples will give 1000 bins, from -50.0 to 49.9.

dfreq = 1/data_stime
range = (-dfreq*data_stime*data_srate/2 , dfreq*data_stime*data_srate/2 - dfreq)
      = (-data_srate/2                  , data_srate/2 - dfreq                 )

IN SHORT
That seems more complicated than it needs to be, but it was the thought process that helped me arrive at a better solution. After doing the math and comparisons I find that there is no need to do all these calculations. The sampling rate only needs to be applied to the freq bins, similar to dividing the x-axis array by the rate when plotting the data. Squaring the FFT values helps accentuate the peaks.

    data = []       #array to hold data read from file
    srate=2.        #sample rate
    samples = 0     #counter for the number of lines in file (# of data samples)
    with open(filename, 'r') as rawfile:
        for i, line in enumerate(rawfile):
            data.append(float(line))
        samples = i + 1

    x = arange(samples)/srate

    # PLOT THE ORIGINAL DATA READ FROM FILE
    plt.plot(x, data)
    plt.show()

    # APPLY FFT
    FFT = fft(data)
    freqs = fftfreq(samples) * srate
    print 'bin range=', [freqs.min(), freqs.max()]
    print 'bin interval=', srate/samples

    # PLOT THE POSITIVE HALF OF FREQ VALUES
    plt.plot(freqs[:samples/2], (abs(FFT.real)**2)[:samples/2], 'g*')
    plt.show()