About the Books

In 1822, Jean-Baptiste Joseph Fourier published his groundbreaking memoir, Théorie Analytique de la Chaleur (The Analytical Theory of Heat). In it, he proposed that:

“Any function of a variable, whether continuous or discontinuous, can be expanded as a series of sines of multiples of the variable.”

How the Fourier Series Works guides you intuitively and systematically through each of the core concepts making up the Fourier Series.

Although Fourier's memoir is highly regarded now, when he originally presented it, eminent mathematicians like Joseph-Louis Lagrange and Pierre-Simon Laplace challenged Fourier’s ideas. What was it they were objecting to?

Fourier claimed that any function could be expanded as a series of sines. A function is another name for a signal. So, according to Fourier, it should be possible to build any signal out of a series of sinusoids. However, this is not the case. The Fourier Series can only model repeating signals.

It took the further work of the German mathematician, Peter Gustav Lejeune Dirichlet, to expand the capabilities of the Fourier Series so that it could model non-repeating signals.

How the Fourier Transform Works follows the development of the Fourier Series into what is now known as the Fourier Transform and beyond.

We find out how the Fourier Transform models non-repeating signals and just what sort of signals it can and can't model.  We then continue the journey right up to the present day through the DTFT and DFT, culminating in a detailed study of how the FFT works.

These book take a visual approach, granting you an thorough and intuitive understanding of Fourier’s ideas; providing you with the basis you need to confidently use one of the cornerstones of modern signal analysis.

The Fourier Series, and its later developments: the Fourier Transform and the Fast Fourier Transform, lie at the heart of so many of our electronic devices. From the mobile phone in your pocket, to early warning systems that keep aircraft engines running safely, Fourier is there, revealing which sine waves are present in the signal.

By taking a visual approach, these books grant you an intuitive understanding of Fourier’s ideas, providing you with the basis you need to use one of the cornerstones of signal analysis.

“Clear, concise and easy-to-grasp complex nuance of the Fourier Series. Excellent book for those new to Fourier or those looking for a refresher.”

— Jason

“This book finally helped me to look right through the black box of Fourier series formula. What an amazing approach!”

— Satish

“This book takes you from where you are to where you want to go. Too clear to go off course. Every word is dead on perfect.”

— Cnc