## 2 Materials and Methods
### Quantification of NR Effects on Stimuli  
The current study used two spectral subtraction-based NR algorithms [40; 41]: one with a minimum mean-square error (MMSE) estimator (hereafter referred to as NR 1) and the other algorithm (hereafter referred to as NR 2) that extends the MMSE estimation to the log-spectral domain to further attenuate noise. These Ephraim-Malah NR algorithms [40; 41] are known for having relatively few artifacts in the residual noise (i.e., stochastic musical noise phenomenon), low computational load, and no dependence on previously learned noise sets ([PERSON], 1994; [PERSON], 2001). Both NR algorithms process the input signal frame by frame, with each 20-ms frame defined using the Hamming window. They start by applying a fast Fourier transform (FFT) and calculating the magnitude spectrum of the short-time frame, followed by estimating a priori and a posteriori SNR to determine the spectral gain for each frame, and then apply the inverse FFT to convert the signal into the temporal domain [for the detailed process, see Figure 2 with notation adopted from [PERSON] (1994); [PERSON] (2001)]. These modified spectral-subtraction algorithms were implemented in several digital hearing aids [e.g., [PERSON], [PERSON] (42), [PERSON], [PERSON] (43)] and have provided foundational work for applying contemporary machine learning techniques to NR [e.g., [PERSON], [PERSON] (44)]. Accurate quantification of the SNR improvement and the speech distortion induced by the NR algorithms is critical to gaining a comprehensive understanding of how these NR algorithms affect changes in behavioral and physiological outcomes [45]. The phase-inversion technique [46] was employed to measure the SNR after applying NR. This approach, commonly used in hearing-aid studies [20; 47; 48], combines two NR-processed noisy signals that are identical but have a different (inverted) noise phase. By adding or subtracting two outputs, the post-NR speech signal and noise stimuli were extracted and used to measure SNR changes. Further, the degree of spectral distortion driven by NR was evaluated using the magnitude-squared coherence method [49]. This spectral analysis technique is frequently used in studies of signal-processing schemes [e.g., [PERSON] and [PERSON] (50), [PERSON], [PERSON] (51), [PERSON], [PERSON] (52)] to assess the coherence between input and output signals in a range from zero to one, where zero indicates two signals are totally different and one indicates they are identical. The current study measured the spectral coherence between NR-processed _speech_ stimulus extracted by the phase-inversion method and unprocessed _speech_ stimulus. Figure 1: Stimulus and electroencephalographic recording structure of the speech-in-noise task. The target word (for example, a monosyllabic word like “sat”) is presented a half second after the noise onset. Individuals’ neural signal-to-noise ratio (SNR) is calculated based on the ratio (b/a) of peak amplitude of temporal envelopes obtained from cortical auditory-evoked responses within a time window (gray colored period in the bottom panel) following the word and noise onset, respectively. Figure 3 illustrates how both NR algorithms affect speech and noise stimuli when a target word is embedded in stationary speech-shaped noise that mimics the spectral properties of speech stimuli at 0 dB SNR. In the current study, NR 1 and NR 2 provided about a 3.5-dB and a 5-dB increase in SNR calculated based on the _unweighted_ long-term RMS levels, respectively. The spectral coherence, which averaged up to 22 kHz between a pair of unprocessed and NR-processed speech stimuli, was around 0.60 and 0.26 for NR 1 and NR 2, respectively, showing that NR 2 provides _stronger noise attenuation_ but induces _more spectral distortion_ in speech than NR 1. Figure 3: Illustration of the effect of noise reduction (NR) algorithms on speech and noise stimuli. (**A**). Power spectral density of speech (solid line) and noise stimuli (dotted line) in each condition is compared.