How can I interpret the output of indexing an fft in python?

Question

I am looking to determine whether a given audio file contains a certain frequency, similar to this question. However, as a beginner, I need help understanding the output.

If I am understanding the linked question correctly, we start by observing the fftfreq output, which is the x axis if understood graphically. Since my sampling rate is 44kHz, the fftfreq contains approximately 22,000 bins. If I wanted to query what magnitude occurred at 800hz, I would simply access value = fftfreq_output[800], then index the actual fft values using this new value like so: fft_output[value]. However, I am confused by the values that are returned. My code is below:

from scipy.io import wavfile
from scipy.fft import fft, fftfreq
from matplotlib import pyplot as plt
import numpy as np
import pandas as pd
user_in = input("Please enter the relative path to your wav file --> ")
sampling_rate, data = wavfile.read(user_in)
print("sampling rate:", sampling_rate)
duration = len(data) / float(sampling_rate)
print("duration:", duration)
number_samples_in_seg = int(sampling_rate * duration)
fft_of_data = fft(data)
fft_bins_from_data = fftfreq(number_samples_in_seg, 1 / sampling_rate)
fft_bins_from_data = fft_bins_from_data[0:number_samples_in_seg//2]
fft_of_data = abs(fft_of_data[0:number_samples_in_seg//2])
value = fft_bins_from_data[800]
print(value)
output = fft_of_data[int(value)]
print(output)

inputing a random wav file of a conversation, my output is this:

6.1500615006150054
71544.37927836686

My questions are:

1. Am I properly indexing the fft_output?

2. How can I interpret these numbers to observe what is the magnitude of the signal at a frequency of 800hz?

Thank you for any help.

Answer 1

no, it's the other way around: value contains the frequency that the 800th entry in your FFT represents.

Honestly, fftfreqs is not ... useful. An FFT of length $N$ always divides the sample rate in $N$ equal pieces, $\Delta f = \frac{f_{\text{sample}}}N$. With 0Hz being the 0.th element, and the $k$th element representing frequency $k\cdot \Delta f$.

So, if you want to know which bin represents a frequency $f$, you just divide that by $\Delta f = \frac{f_{\text{sample}}}N$ to get the number of the bin you should look into. Division by $\frac{f_{\text{sample}}}N$ is the same as multiplication by $\frac N{f_{\text{sample}}}$.

So, not quite sure why there's a function for that.