What’s a good book on multi-rate dsp?
Assuming you have completed the basic course in DSP with a book like Oppenheim's Discrete-Time Signal Processing book then the next step could be anyone of the followings: 

Multiresolution Signal Decomposition: Transforms, Subbands,Wavelets, A.Akansu

Multirate Digital Signal Processing, Rabiner

Multirate Systems and Filter Banks, P.P.Vaidyanathan

Wavelets and Filter Banks, Gilbert Strang

Multidimensional Digital Signal Processing, Dudgeon

Subband Adaptive Filtering: Theory and Implementation", by Woon-Seng Gan, Kong-Aik Lee, Sen M. Kuo

Wavelets and subband coding, Vetterli

Advanced DSP, John G Proakis

For a good book on multi rate DSP from communications perspective, please refer to the book below

Multi rate signal processing for communication systems, Friedrich J Harris

For a MATLAB specific handling, please refer to the book below

Multirate Filtering for Digital Signal Processing: MATLAB Applications, Ljiljana Milic

Personal recommendation the books by Vetterli and Fredrich Harris