Amplitude modulation coefficient \(R_{\text {AM}}\) for the plane, turbulent wall jet (henceforth wall jet) data published by Gupta et al. (J Fluid Mech 891:A11 [1]) is computed using Hilbert transform method (a combination of Fourier and Hilbert transforms) and compared with the \(R_{\text {AM}}\) data from Bhatt and Gnanamanickam (Phys Rev Fluids 5:74604 [2]) at matching Reynolds numbers (Re \(_\tau \) as well as Re \(_\delta \) ). Discrepancies between the two curves are discussed with focus on lateral confinement of the wall jet. Wavelet transform method (a combination of Fourier and wavelet transforms) is also used to compute \(R_{\text {AM}}\) and validated against the Hilbert transform method calculations. Furthermore, wavelet transform method is used to compute the frequency modulation coefficient \(R_{\text {FM}}\) . Results for \(R_{\text {AM}}\) and \(R_{\text {FM}}\) computed for the three Re \(_j\) experiments reported by Gupta et al. (J Fluid Mech 891:A11 [1]) display Reynolds number similarity of the amplitude and frequency modulation in wall jets over the range of Reynolds numbers covered.