For those who are interested in signal processing, the classic Wavelets and Subband Coding by Martin Vetterli and Jelena Kovačević is a must-have. But perhaps you were unaware that the two of them, together with Vivek Goyal have written a pair of books:
Signal Processing: Foundations
Signal Processing: Fourier and Wavelet Representations
They should give you a solid grounding the fundamentals of signal processing from a more modern perspective. Preliminary versions are available for download from the book’s website.