Summability methods for trigonometric Fourier series play a fundamental role in approximation theory and signal processing. Among them, Fejér means provide a classical regularization tool ensuring uniform convergence for continuous functions. In this paper, we investigate an operator constructed as the arithmetic mean of the first $n$ Fejér means. This approach leads to an additional averaging procedure and naturally strengthens the smoothing effect compared to a single Fejér mean of the same order. The operator is studied both in the time and frequency domains. In the time domain, it is represented as a convolution operator with a positive summability kernel. Its normalization and structural properties are established, including preservation of constants and removability of the singularity at the origin. In the frequency domain, the operator is described via its Fourier multipliers, obtained as averages of the corresponding Fejér multipliers. Their monotonic decay with respect to the harmonic index is analyzed, which provides insight into the enhanced attenuation of high-frequency components. A discrete (interpolation-type) analogue defined on a uniform grid is also introduced and interpreted as a quadrature approximation of the continuous convolution representation. Explicit representations of the operator and its kernel are derived. The smoothing character of the method is justified theoretically and confirmed numerically for periodic signals with additive noise. The experiments demonstrate improved suppression of high harmonics compared to classical Fejér summation of the same order. The proposed operator can be regarded as a strengthened low-pass Fourier multiplier method and may be effectively applied to smoothing and filtering of one-dimensional periodic signals.
