I am new to signal processing domain. When I run fft on data of length 1000, I get 1000 complex numbers. Now, if I want to extract the low frequency information or signal approximation, I take the first few elements(say 50) of the array and also the same number of elements from the last(as it is symmetric). Excluding these values, i put everything as 0 and take inverse fft and I get back the approximation of the original signal. Now, having done the above, I take back the original array of 1000 complex numbers, put the first 50 and last 50 numbers as 0, and then repeat the process on the remaining values to get successive higher frequency information. My main goal is that I want to separately extract low frequency and high frequency information from the signal(like in wavelet). Is my approach correct?
Unless you fully understand the math behind the DFT, you are likely to run into problems like circular vs linear convolution, time domain aliasing, excessive time domain ringing, etc.
For "light weight" frequency selectivity application, time domain filter is typically a lot easier.