Discrete wavelet transform; how to interpret approximation and detail coefficients?

1. What is approximation and detail coefficients in wavelet transform?
2. What do the coefficients of the wavelet transform mean?
3. What is coefficient approximation?
4. How do you read wavelet transform?

What is approximation and detail coefficients in wavelet transform?

Coefficients (weights) associated with the scaling function, called approximation coefficients, capture low frequency information, while coefficients associated with wavelet function, called detail coefficients, capture high-frequency information.

What do the coefficients of the wavelet transform mean?

The wavelet transform is the convolution of a function (data) with a wavelet base. The result of this convolution is the wavelet coefficients. Convolution measures the similarity between the wavelet function and the data. If the similarity is high then you will have peaks.

What is coefficient approximation?

The approximation, or scaling, coefficients are the lowpass representation of the signal and the details are the wavelet coefficients. At each subsequent level, the approximation coefficients are divided into a coarser approximation (lowpass) and highpass (detail) part.

How do you read wavelet transform?

The basic idea behind wavelet transform is, a new basis(window) function is introduced which can be enlarged or compressed to capture both low frequency and high frequency component of the signal (which relates to scale).