Fig. 7

Time-domain (a–d) and frequency-domain (e–h) representation of ultrasound echoes to illustrate the difference between radiofrequency (RF), in-phase (I), and quadrature (Q) datasets. a The radiofrequency signal corresponds to the ultrasound echo at a given scan line on an image. b The demodulated in-phase and (c) quadrature components are obtained through signal processing implying multiplication of the RF signal by cosine (I) and sine (Q) functions at the center frequency of the probe, or of the transmitted wave. d The envelope detected echo used to produce a B-mode image by mapping the magnitude (red envelope) as a function of depth in gray scale is obtained as the square root of I² plus Q². Advanced materials: e Frequency-domain representation of the RF signal, where the bandwidth of interest is governed by the ultrasound transducer characteristics. The Nyquist frequency is the minimum sampling frequency of the temporal signal required to avoid aliasing (i.e., an undersampling of the echo resulting in a wrong representation of the signal). Here a 2.5 MHz center frequency probe is considered with a bandwidth covering the frequency range of 1.25–3.75 MHz. f I/Q demodulation in the frequency domain (one needs to know that the Fourier transform of a temporal signal used to obtain its power spectrum results in a real—positive frequency, and imaginary—negative frequency display since it is a complex number representation). g The demodulation is followed by the use of a low-pass (LP) filter to keep frequency contents corresponding to the original main positive spectrum of the RF signal. By applying an inverse Fourier transformation on the final spectral representation, one obtains the temporal I and Q complex signals. h For the example of this figure, the demodulation allowed reducing the sampling rate by a factor of 6. Adapted from [28]