## Posts Tagged 'Fourier analysis'

### Making Sound Pictures to Identify Bird Songs

Top: Audio signal with three chirps. Bottom: Time-Frequency spectrogram of signal.

A trained musician can look at a musical score and imagine the sound of an entire orchestra. The score is a visual representation of the sounds. In an analogous way, we can represent birdsong by an image, and analysis of the image can tell us the species of bird singing. This is what happens with Merlin Bird ID. In a recent episode of Mooney Goes Wild, Niall Hatch of Birdwatch Ireland interviewed Drew Weber of the Cornell Lab of Ornithology, a developer of Merlin Bird ID. This phone app enables a large number of birds to be identified [TM237 or search for “thatsmaths” at irishtimes.com].

### Joseph Fourier and the Greenhouse Effect

Jean-Baptiste Joseph Fourier, French mathematician and physicist, was born in Auxerre 251 years ago today. He is best known for the mathematical techniques that he developed in his analytical theory of heat transfer. Over the past two centuries, his methods have evolved into a major subject, harmonic analysis, with widespread applications in number theory, signal processing, quantum mechanics, weather prediction and a broad range of other fields [TM159 or search for “thatsmaths” at irishtimes.com].

Greenhouse Effect [Image Wikimedia Commons]

### Don’t be Phased by Waveform Distortions

For many years there has been an ongoing debate about the importance of phase changes in music. Some people claim that we cannot hear the effects of phase errors, others claim that we can. Who is right? The figure below shows a waveform of a perfect fifth, with components in the ratio ${3 : 2}$ for various values of the phase-shift. Despite the different appearances, all sound pretty much the same.

Continue reading ‘Don’t be Phased by Waveform Distortions’