This work analyzes the constant-Q filterbank-based time-frequency representations for speech emotion recognition (SER). Constant-Q filterbank provides non-linear spectrotemporal representation with higher frequency resolution at low frequencies. Our investigation reveals how the increased low-frequency resolution benefits SER. The time-domain comparative analysis between short-term mel-frequency spectral coefficients (MFSCs) and constant-Q filterbank-based features, namely constant-Q transform (CQT) and continuous wavelet transform (CWT), reveals that constant-Q representations provide higher time-invariance at low-frequencies. This provides increased robustness against emotion irrelevant temporal variations in pitch, especially for low-arousal emotions. The corresponding frequency-domain analysis over different emotion classes shows better resolution of pitch harmonics in constant-Q-based time-frequency representations than MFSC. These advantages of constant-Q representations are further consolidated by SER performance in the extensive evaluation of features over four publicly available databases with six advanced deep neural network architectures as the back-end classifiers. Our inferences in this study hint toward the suitability and potentiality of constant-Q features for SER.