Discrete Wavelet Transform - Visualizing Relation between Decomposed Detail Coefficients and Signal

1. What are coefficients in DWT?
2. What is approximation and detail coefficients in wavelet transform?
3. What is decomposition level of wavelet transform?
4. What is wavelet decomposition and reconstruction?

What are coefficients in DWT?

The DWT coefficients represent the degree of correlation between the analyzed signal and the wavelet function at different instances of time; therefore, DWT coefficients contain temporal information of the analyzed signal.

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 is decomposition level of wavelet transform?

Based on Ref. [20], the decomposition level for each wavelet family is set to 1. Compared to other wavelet families the coiflet wavelets clearly show the patterns of the t–f image in H, V, and D images rather than the other wavelets, respectively.

What is wavelet decomposition and reconstruction?

The wavelet decomposition and reconstruction algorithm of finite length signal. Abstract: A wavelet algorithm of finite signals associated with Mallat's (1989) wavelet algorithm is proposed. It uses only finite wavelet bases without periodically extending signals, allowing perfect reconstruction of signals.